Updated on 2022/10/02

写真a

 
MIURA Takeshi
 
Organization
Academic Assembly Institute of Science and Technology Fundamental Sciences Professor
Graduate School of Science and Technology Fundamental Sciences Professor
Faculty of Science Department of Science Professor
Title
Professor
External link

Degree

  • 博士(理学) ( 2000.3   新潟大学 )

Research Interests

  • 微分方程式の安定性

  • 可換Banach環論

  • スペクトル保存写像

  • Spectra preserving maps

  • Stability of differential equations

  • Commutative Banach algebras

Research Areas

  • Natural Science / Basic analysis

Research History (researchmap)

  • Niigata University   Professor

    2013.4

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  • Professor,Graduate School of Science and Engineering ,Yamagata University

    2010.4

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  • Yamagata University   Graduate School of Science and Engineering

    2010.4 - 2013.3

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  • Associate Professor,Graduate School of Science and Engineering ,Yamagata University

    2007.4 - 2010.3

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  • Yamagata University   Graduate School of Science and Engineering

    2007.4 - 2010.3

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  • Associate Professor,Faculty of Engineering,Yamagata University

    2005.4 - 2007.3

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  • Yamagata University   Faculty of Engineering, Faculty of Engineering

    2005.4 - 2007.3

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  • Associate Professor,International Student Center,Yamagata University

    2005.4 - 2006.3

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  • 山形大学留学生センター 助教授

    2005.4 - 2006.3

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  • Associate Professor,International Student Center,Yamagata University

    2003.4 - 2005.3

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  • 山形大学留学生センター 助教授

    2003.4 - 2005.3

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  • Yamagata University   Faculty of Engineering, Faculty of Engineering

    2001.4 - 2003.3

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  • Lecturer,Faculty of Engineering,Yamagata University

    2001.4 - 2003.3

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Research History

  • Niigata University   Faculty of Science Department of Science   Professor

    2017.4

  • Niigata University   Graduate School of Science and Technology Fundamental Sciences   Professor

    2013.4

  • Niigata University   Graduate School of Science and Technology Fundamental Sciences   Professor

    2013.4

  • Niigata University   Abolition organization Mathematical Analysis   Professor

    2013.4 - 2017.3

Professional Memberships

Committee Memberships

  • 日本数学会   関数環グループ代表者  

    2010.12   

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    Committee type:Academic society

    日本数学会

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  • 日本数学会   実解析学グループ責任者  

    2007.4 - 2009.3   

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    Committee type:Academic society

    日本数学会

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Papers

  • Semigroup operations distributed by natural noncancellative semigroup operations on the positive real numbers Reviewed

    H. Oka, T. Miura, S.-E. Takahasi

    Semigroup Forum   to appear   2020

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  • Characterization of distributive semigroup operation onthe positive real numbers Reviewed

    S.-E. Takahasi, T. Miura, H. Oka

    Semigroup Forum   2020

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  • 2-local isometries on C^(n)([0,1]) Reviewed

    K. Kawamura, H. Koshimizu, T. Miura

    Contemp. Math.   737   119 - 124   2019

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  • Corrigendum to ``Examples of generalized bi-circular idempotnts on spaces of continuously differentiable functions" Reviewed

    F. Botelho, T. Miura

    J. Math. Anal. Appl.   474   1481 - 1487   2019

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  • Classification of semisimple commutative Banach algebras of type I Reviewed

    J. Inoue, T. Miura, H. Takagi, S.-E. Takahasi

    Nihonkai Math. J   30   1 - 17   2019

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  • Examples of generalized bi-circular idempotents on spaces of continuously differentiable functions Reviewed

    Fernanda Botelho, Takeshi Miura

    Journal of Mathematical Analysis and Applications   465 ( 2 )   795 - 802   2018.9

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Academic Press Inc.  

    In this note we investigate the form of a class of idempotents, called generalized bi-circular idempotents on spaces of continuously differentiable functions defined on the interval [0,1] and with values in the complex numbers.

    DOI: 10.1016/j.jmaa.2018.05.022

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  • Norms on C1([0, 1]) and their isometries Reviewed

    Kazuhiro Kawamura, Hironao Koshimizu, Takeshi Miura

    Acta Scientiarum Mathematicarum   84 ( 1-2 )   239 - 261   2018

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:University of Szeged  

    We present a unified framework to study isometries, with respect to various norms, on C1([0, 1]), the space of continuously first differentiable functions on the unit interval [0, 1]. We also discuss continuous deformations of isometry groups induced by perturbations of norms on C1([0, 1]).

    DOI: 10.14232/actasm-017-331-0

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  • Surjective isometries on a Banach space of analytic functions on the open unit disc Reviewed

    T. Miura, N. Niwa

    Nihonkai Math. J.   29   51 - 65   2018

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  • Real-linear surjective isometries between function spaces Reviewed

    Kazuhiro Kawamura, Takeshi Miura

    TOPOLOGY AND ITS APPLICATIONS   226   66 - 85   2017.8

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ELSEVIER SCIENCE BV  

    We study surjective isometries between subspaces of continuous functions containing all constant functions and separating the points of the underlying spaces. In many contexts, every such isometry is represented by a combination of a weighted composition operator and its complex conjugate, called the canonical form, while there exists an isometry which does not take such a form ([14]). We seek a topological condition on compact Hausdorff spaces such that every surjective isometry on function spaces over the spaces has the canonical form. Also we extend the construction of [14] to show that, if a compact metrizable space X admits a semi free action of the circle group with a global section, then there exists an isometry of a function space on X which does not take the canonical form. (C) 2017 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.topol.2017.05.002

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  • A Characterization of Multipliers of a Lau Algebra Constructed by Semisimple Commutative Banach Algebras Reviewed

    Sin-Ei Takahasi, Hiroyuki Takagi, Takeshi Miura

    TAIWANESE JOURNAL OF MATHEMATICS   20 ( 6 )   1401 - 1415   2016.12

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:MATHEMATICAL SOC REP CHINA  

    A necessary and sufficient condition for a Lau type binary operation defined by two mappings to be an algebra-operation is given in terms of multipliers. Also a characterization of multipliers of a Lau algebra constructed by semisimple commutative Banach algebras is given in terms of multipliers of original Banach algebras.

    DOI: 10.11650/tjm.20.2016.7386

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  • Mappings onto multiplicative subsets of function algebras and spectral properties of their products Reviewed

    Takeshi Miura, Thomas Tonev

    ARKIV FOR MATEMATIK   53 ( 2 )   329 - 358   2015.10

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER  

    We characterize mappings S (i) and T (i) , not necessarily linear, from sets , i=1,2, onto multiplicative subsets of function algebras, subject to the following conditions on the peripheral spectra of their products: sigma (pi) (S (1)(a)S (2)(b))aS,sigma (pi) (T (1)(a)T (2)(b)) and sigma (pi) (S (1)(a)S (2)(b))a (c)sigma (pi) (T (1)(a)T (2)(b))not equal a..., , . As a direct consequence we obtain a large number of previous results about mappings subject to various spectral conditions.

    DOI: 10.1007/s11512-014-0210-y

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  • Surjective isometries between function spaces Reviewed

    Takeshi Miura

    FUNCTION SPACES IN ANALYSIS   645   231 - 239   2015

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:AMER MATHEMATICAL SOC  

    Let X be a compact Hausdorff space. We denote by C(X) the Banach space of all continuous complex valued functions on X with respect to the supremum norm. A function space A on X is a normed linear subspace of C(X) that contains the constant function 1 and separates the points of X. We give a necessary and sufficient condition for a surjective distance preserving map between two function spaces be represented by a weighted composition operator.

    DOI: 10.1090/conm/645/12926

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  • Ulam type stability problems for alternative homomorphisms Reviewed

    Sin-Ei Takahasi, Makoto Tsukada, Takeshi Miura, Hiroyuki Takagi, Kotaro Tanahashi

    JOURNAL OF INEQUALITIES AND APPLICATIONS   2014.6

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER INTERNATIONAL PUBLISHING AG  

    We introduce an alternative homomorphism with respect to binary operations and investigate the Ulam type stability problem for such a mapping. The obtained results apply to Ulam type stability problems for several important functional equations.

    DOI: 10.1186/1029-242X-2014-228

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  • Real-linear isometries between subspaces of continuous functions Reviewed

    Hironao Koshimizu, Takeshi Miura, Hiroyuki Takagi, Sin-Ei Takahasi

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   413 ( 1 )   229 - 241   2014.5

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ACADEMIC PRESS INC ELSEVIER SCIENCE  

    Let X and Y be locally compact Hausdorff spaces. Let A and B be complex-linear subspaces of C-0(X) and C-0(Y), respectively. Suppose that for each triple of distinct points x, x', x" epsilon X, there exists f epsilon A such that vertical bar f(x)vertical bar not equal vertical bar f(x')vertical bar and f (x") = 0. Also suppose that for each pair of distinct points y, y' epsilon Y. there exists g epsilon B such that vertical bar g(y)vertical bar not equal vertical bar g(y')vertical bar. For such A and B, we prove the following statement: If T is a real-linear isometry of A onto B, then there exist an open and closed subset E of ChB, a homeomorphism phi of ChB onto Ch A and a unimodular continuous function omega on ChB such that Tf = omega(f o phi) on E and Tf = omega(f o phi) on ChB\E for all f epsilon A, where Ch A and ChB are the Choquet boundaries for A and B, respectively. Moreover, we remark that the separation condition on A cannot be omitted in the above result. (C) 2013 Elsevier Inc. All right's reserved.

    DOI: 10.1016/j.jmaa.2013.11.050

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  • Real linear isometries between function algebras. II Reviewed

    Osamu Hatori, Takeshi Miura

    CENTRAL EUROPEAN JOURNAL OF MATHEMATICS   11 ( 10 )   1838 - 1842   2013.10

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    We describe the general form of isometries between uniformly closed function algebras on locally compact Hausdorff spaces in a continuation of the study by Miura. We can actually obtain the form on the Shilov boundary, rather than just on the Choquet boundary. We also give an example showing that the form cannot be extended to the whole maximal ideal space.

    DOI: 10.2478/s11533-013-0282-0

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  • A CHARACTERIZATION OF THE STABILITY OF A SYSTEM OF THE BANACH SPACE VALUED DIFFERENTIAL EQUATIONS Reviewed

    Takeshi Miura, Go Hirasawa, Sin-Ei Takahasi, Takahiro Hayata

    MATHEMATICAL INEQUALITIES & APPLICATIONS   16 ( 3 )   717 - 728   2013.7

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ELEMENT  

    We will consider the Banach space valued differential equation eta'(t) = A eta(t), where A is an n x n complex matrix. We give a necessary and sufficient condition in order that the equation have the Hyers-Ulam stability. As a Corollary, we prove that the Banach space valued linear differential equation with constant coefficients y((n))(t) + a(n-1)y((n-1))(t) + ... + a(1)y'(t) + a(0)y(t) = 0 has the Hyers-Ulam stability if and only if Re lambda not equal 0 for all the solutions lambda of the equation z(n) + a(n-1)z(n-1) + ... + a(1)z + a(0) = 0.

    DOI: 10.7153/mia-16-54

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  • Isometries and maps compatible with inverted Jordan triple products on groups Reviewed

    Osamu Hatori, Go Hirasawa, Takeshi Miura, Lajos Molnár

    Tokyo Journal of Mathematics   35 ( 2 )   385 - 410   2012.12

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    Motivated by the famous Mazur-Ulam theorem in this paper we study algebraic properties of isometries between metric groups. We present some general results on so-called d-preserving maps between subsets of groups and apply them in several directions. We consider d-preserving maps on certain groups of continuous functions defined on compact Hausdorff spaces and describe the structure of isometries between groups of functions mapping into the circle group T. Finally, we show a generalization of the Mazur-Ulam theorem for commutative groups and present a metric characterization of normed real-linear spaces among commutative metric groups.

    DOI: 10.3836/tjm/1358951327

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  • Stability of the Banach space valued Chebyshev differential equation Reviewed

    Takeshi Miura, Sin-Ei Takahasi, Takahiro Hayata, Kotaro Tanahashi

    APPLIED MATHEMATICS LETTERS   25 ( 11 )   1976 - 1979   2012.11

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    We prove that, if f is an approximate solution of the Banach space valued Chehyshev differential equation (1 - x(2))y ''(x) - xy'(x) + n(2)y(x) = 0 for x is an element of (-1, 1), then f is near to an exact solution. (C) 2012 Elsevier Ltd. All rights reserved.

    DOI: 10.1016/j.aml.2012.03.012

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  • Real-linear isometries between function algebras

    Takeshi Miura

    CENTRAL EUROPEAN JOURNAL OF MATHEMATICS   9 ( 4 )   778 - 788   2011.8

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    Let A and B be uniformly closed function algebras on locally compact Hausdorff spaces with Choquet boundaries Ch A and ChB, respectively. We prove that if T: A -> B is a surjective real-linear isometry, then there exist a continuous function kappa: ChB -> {z a a",: |z| = 1}, a (possibly empty) closed and open subset K of ChB and a homeomorphism phi: ChB -> ChA such that T(f) = kappa(f a similar to phi) on K and T(f) = kappa (f.phi) over bar on ChB \ K for all f a A. Such a representation holds for surjective real-linear isometries between (not necessarily uniformly closed) function algebras.

    DOI: 10.2478/s11533-011-0044-9

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  • Sprctral radii conditions for isomorphisms between unital semisimple commutative Banach algebras Reviewed

    G. Hirasawa, T. Miura, H. Takagi

    Contemp Math.   547   125 - 134   2011.1

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  • Spectral Preservers in Commutative Banach Algebras Reviewed

    Osamu Hatori, Scott Lambert, Aaron Luttman, Takeshi Miura, Thomas Tonev, Rebekah Yates

    FUNCTION SPACES IN MODERN ANALYSIS   547   103 - +   2011

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    A spectral preserver is a map between Banach algebras such that some properties or objects connected with the spectra of algebra elements are invariant under its action. Though such maps have been studied extensively in the operator algebra setting, only during the last decade have they been systematically analyzed in commutative Banach algebras. This article is a survey of recent investigations on spectral preserver problems in commutative Banach algebras, including some history, basic results, future directions and open problems.

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  • An equality condition of Arhippainen-Müller's estimate and its related problem Reviewed

    Sin-Ei Takahasi, Takeshi Miura, Takahiro Hayata

    Taiwanese Journal of Mathematics   15 ( 1 )   165 - 169   2011

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:Mathematical Society of the Rep. of China  

    J. Arhippainen and V.M̈uller showed that ||a + λe|| 1 ≤ 3 ||a + λe|| op for all a + λe || A ̃, where A ̃ is the unitization of an arbitrary non-unital Banach algebra A with regular norm. In this note, we present a necessary and sufficient condition for the equality of this estimate and its related problem.

    DOI: 10.11650/twjm/1500406167

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  • Divisibly norm-preserving maps between commutative banach algebras Reviewed

    Takeshi Miura, Dai Honma, Rumi Shindo

    Rocky Mountain Journal of Mathematics   41 ( 5 )   1675 - 1699   2011

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    Let A and B be unital commutative Banach algebras. Suppose that A is semi-simple. Let ρ : A → A and τ : B → B be bijections. If T : A → B is a surjection with, for some α ∈ C \\ {0}, r ( T (f) r ( T ( s ) ) - α) = r ( f ρ( g ) - α) for all f,g ∈ A, then B is semi-simple and r ( T ( f ) T ( g )-1 - 1) = r(fg-1 - 1) for every f ∈ A and G ∈ A-1. As a consequence, T ( 1 ) is invertible and T ( 1 )-1 T is a real-algebra isomorphism. If, in addition, T(1)-1T(i) = i, then T ( 1 )T is a complexalgebra isomorphism. This result unifies and generalizes [3, Theorem 7.4] and [4, Theorem 3.2 and 6.2]. Copyright © 2011 Rocky Mountain Mathematics Consortium.

    DOI: 10.1216/RMJ-2011-41-5-1675

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  • Generalizations of spectrally multiplicative surjections between uniform algebras Reviewed

    Osamu Hatori, Takeshi Miura, Rumi Shindo, Hiroyuki Takagi

    Rendiconti del Circolo Matematico di Palermo   59 ( 2 )   161 - 183   2010.8

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    Let A and B be unital semisimple commutative Banach algebras. It is shown that if surjections S,T: A → B with S(1) = T(1) = 1 and α ∈ ℂ\\ {0} satisfy r(S(a)T(b) - α)= r(ab- α) for all a,b ∈ A then S = T and S is a real algebra isomorphism, where r(a) is the spectral radius of a. Let I be a nonempty set, A and B be uniform algebras. Let ρ, τ: I → A and S,T: I → B be maps satisfying σπ (S(p)T(q)) ⊂ σπ (ρ(p) τ(q)) for all p,q ∈ I, where σπ (f) is the peripheral spectrum of f. Suppose that the ranges ρ(I), τ(I) ⊂ A and S(I),T(I) ⊂ B are closed under multiplication in a sense, and contain peaking functions "enough". There exists a homeomorphism φ: Ch(B)→Ch(A) such that S(p)(y)= ρ(p)(φ(y)) and T(p)(y)= τ(p)(φ(y)) for every p ∈ I and y ∈ Ch(B), where Ch(A) is the Choquet boundary of A. © 2010 Springer-Verlag Italia.

    DOI: 10.1007/s12215-010-0013-3

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  • Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras Reviewed

    Osamu Hatori, Go Hirasawa, Takeshi Miura

    CENTRAL EUROPEAN JOURNAL OF MATHEMATICS   8 ( 3 )   597 - 601   2010.6

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    Let A and B be unital, semisimple commutative Banach algebras with the maximal ideal spaces M(A) and M(B), respectively, and let r(a) be the spectral radius of a. We show that if T: A -> B is a surjective mapping, not assumed to be linear, satisfying r(T(a) + T(b)) = r(a + b) for all a; b is an element of A, then there exist a homeomorphism phi : M(B) -> M(A) and a closed and open subset K of M(B) such that
    <(T(a))over cap>(y) = {<(T(e))over cap>(y)(a) over cap(phi(y)) y is an element of K <(T(e))over cap>(y)(a) over cap(phi(y)) y is an element of M(B)\K
    for all a is an element of A, where e is unit element of A. If, in addition, <(T(e))over cap> = 1 and <(T(ie))over cap> = i on M(B), then T is an algebra isomorphism.

    DOI: 10.2478/s11533-010-0025-4

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  • ON A HYERS-ULAM-AOKI-RASSIAS TYPE STABILITY AND A FIXED POINT THEOREM Reviewed

    Sin-Ei Takahasi, T. Miura, H. Takagi

    JOURNAL OF NONLINEAR AND CONVEX ANALYSIS   11 ( 3 )   423 - 439   2010

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:YOKOHAMA PUBL  

    Let X be a set with a binary operation circle and (Y, d) a complete metric space with a binary operation circle. Take a nonnegative function epsilon on X x X, a nonnegative function 6 on X and two mappings f, g : X -> Y. With the aid of Banach's fixed point theorem, we establish two general settings on which the following holds: If d(f (x circle x'), g(x) circle g(x')) <= epsilon(x, x') and d(f (x), g(x)) <= delta(x) for all x, x' is an element of X, then there exists a unique mapping f(infinity) : X -> Y such that f(infinity)(x circle x') = f(infinity)(x) circle f(infinity)(x'), d(f (x), f(infinity)(x)) <= A epsilon(x,x) + B delta(x) and d(g(x), f(infinity)(x)) <= A epsilon(x,x) C delta(x) for all x, x' is an element of X and some finite constants A, B and C. Moreover, we describe various concrete settings to which the above results are applicable. Some of them are the known results.

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  • A generalization of peripherally-multiplicative surjections between standard operator algebras Reviewed

    Takeshi Miura, Dai Honma

    CENTRAL EUROPEAN JOURNAL OF MATHEMATICS   7 ( 3 )   479 - 486   2009.9

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    Let A and B be standard operator algebras on Banach spaces X and Y, respectively. The peripheral spectrum sigma(pi) (T) of T is defined by sigma(pi) (T) = z a sigma(T): |z| = max(wa sigma(T)) |w|. If surjective (not necessarily linear nor continuous) maps phi, I center dot: A -> B satisfy sigma(pi) (phi(S)I center dot(T)) = sigma(pi) (ST) for all S; T a A, then phi and I center dot are either of the form phi(T) = A (1) TA (2) (-1) and I center dot(T) = A (2) TA (1) (-1) for some bijective bounded linear operators A (1); A (2) of X onto Y, or of the form phi(T) = B (1) T*B (2) (-1) and I center dot(T) = B (2) T*B (-1) for some bijective bounded linear operators B (1);B (2) of X* onto Y.

    DOI: 10.2478/s11533-009-0033-4

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  • Peripherally Monomial-Preserving Maps between Uniform Algebras Reviewed

    Osamu Hatori, Kazumi Hino, Takeshi Miura, Hirokazu Oka

    MEDITERRANEAN JOURNAL OF MATHEMATICS   6 ( 1 )   47 - 59   2009.3

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER BASEL AG  

    Let A and B be uniform algebras and p(z, w) = z(m)w(n) a two-variable monomial. We characterize maps T from certain subsets of A into B such that sigma(pi)(p(T(f), T(g))) subset of sigma(pi)(p(f, g)) holds for all f and g in the domain of T; peripherally monomial-preserving maps. Furthermore A and B are proved to be isometrical isomorphic as Banach algebras. If the greatest common divisor of m and n is 1, then T is extended to an isometrical linear isomorphism; a weighted composition operator. An example of peripherally monomial-preserving surjections between uniform algebras which is not linear, nor multiplicative, nor injective is given when the greatest common divisor is strictly greater than 1.

    DOI: 10.1007/s00009-009-0166-5

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  • An estimate of the commutativity of $C^2$-function and probability measure Reviewed

    T. Miura, T. Hayata, S.-E. Takahasi

    J. Math. Inequal.   3   169 - 180   2009.1

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  • Reflections and a generalization of the Mazur-Ulam theorem (accepted) Reviewed

    O. Hatori, K. Kobayashi, T. Miura, S.-E. Takahasi

    Rocky Mountain J. Math.   2009.1

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  • On the root closedness of continuous function algebras Reviewed

    Kazuhiro Kawamura, Takeshi Miura

    TOPOLOGY AND ITS APPLICATIONS   156 ( 3 )   624 - 628   2009.1

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ELSEVIER SCIENCE BV  

    For a compact Hausdorff space X, C(X) denotes the algebra of all complex-valued continuous functions on X. For a positive integer n, we say that C(X) is n-th root closed if, for each f epsilon C(X). there exists g epsilon C(X) such that f = g(n). It is shown that, for each integer m >= 2, there exists a compact Hausdorff space X(m) such that C(X(m)) is m-th root closed, but not n-th root closed for each integer n relatively prime to m. This answers a question posed by Countryman Jr. [R.S. Countryman Jr., On the characterization of compact Hausdorff X for which C(X) is algebraically closed, Pacific J. Math. 20 (1967) 433-438] et al. (C) 2008 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.topol.2008.08.015

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  • Stability of almost multiplicative functionals Reviewed

    N. Niwa, H. Oka, T. Miura, S.-E. Takahasi

    Aust. J. Math. Anal. Appl.   9   1 - 8   2009.1

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  • Peripheral Multiplicativity of Maps on Uniformly Closed Algebras of Continuous Functions Which Vanish at Infinity Reviewed

    Osamu Hatori, Takeshi Miura, Hirokazu Oka, Hiroyuki Takagi

    Tokyo Journal of Mathematics   32 ( 1 )   91 - 104   2009

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    We study maps between uniformly closed algebras of complex-valued continuous functions which vanish at infinity on locally compact Hausdorff spaces. Without assuming linearity nor multiplicativity on the maps we show that they are isometrical isomorphisms as Banach space operators if they satisfy that the peripheral range of the product of the images of any two elements coincides with the peripheral range of the product of those elements. Furthermore, if the underlying algebras contain approximate identities, then they are isometrically isomorphic as Banach algebras, which is a generalization of a recent result of Luttman and Tonev for the case of uniform algebras. On the other hand it is not the case without assuming the existence of approximate identities
    An example is given. © 2009 International Academic Printing Co. Ltd. All rights reserved.

    DOI: 10.3836/tjm/1249648411

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  • Superstability of Generalized Multiplicative Functionals Reviewed

    Takeshi Miura, Hiroyuki Takagi, Makoto Tsukada, Sin-Ei Takahasi

    JOURNAL OF INEQUALITIES AND APPLICATIONS   2009

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    Let X be a set with a binary operation. such that, for each x, y, z. X, either (x circle y) circle z = (x circle z) circle y, or z circle (x circle y) = x circle (z circle y). We show the superstability of the functional equation g(x circle y) = g(x)g(y). More explicitly, if epsilon >= 0 and f : X -> C satisfies |f(x circle y) - f(x)f(y)| <= epsilon for each x, y is an element of X, then f(x circle y) = f(x)f(y) for all x, y is an element of X, or |f(x)| <= (1 + root 1 + 4 epsilon)/2 for all x is an element of X. In the latter case, the constant (1 + root 1 + 4 epsilon)/2 is the best possible. Copyright (C) 2009 Takeshi Miura et al.

    DOI: 10.1155/2009/486375

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  • On surjective ring homomorphisms between semi-simple commutative Banach algebras Reviewed

    T. Miura, S.-E. Takahasi, N. Niwa, H. Oka

    Publ. Math. Debrecen   73   119 - 131   2008.12

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  • Ring homomorphisms on commutative regular Banach algebras Reviewed

    T. Miura, S.-E. Takahasi, N. Niwa

    Nihonkai Math. J.   19   61 - 74   2008.1

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  • A Cauchy-Euler Type Factorization of Operators Reviewed

    Sin-Ei Takahasi, Hirokazu Oka, Takeshi Miura, Hiroyuki Takagi

    Tokyo Journal of Mathematics   31 ( 2 )   489 - 493   2008

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    A Cauchy-Euler type factorization property which is closely related with the Hyers-Ulam stability problem is introduced in the algebra of all linear self maps of a commutative algebra without order. Several examples of linear self maps with such a property are given in this note. © 2008 International Academic Printing Co. Ltd. All rights reserved.

    DOI: 10.3836/tjm/1233844065

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  • An example of multiplicatively spectrum-preserving maps Reviewed

    O. Hatori, T. Miura, H. Oka

    Nihonkai Math. J.   18   11 - 15   2007.12

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  • A perturbation of first order linear differential equation for Banach space-valued holomorphic functions Reviewed

    T. Miura, H. Oka, S.-E. Takahasi, N. Niwa

    J. Math. Inequal.   1   377 - 385   2007.9

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  • 2-local isometries and 2-local automorphisms on uniform algebras Reviewed

    Osamu Hatori, Takeshi Miura, Hirokazu Oka, Hiroyuki Takagi

    Hikari Ltd.   2   2491 - 2502   2007.7

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  • Exponential type functional equation and its Hyers-Ulam stability Reviewed

    Sin-Ei Takahasi, Takeshi Miura, Hiroyuki Takagi

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   329 ( 2 )   1191 - 1203   2007.5

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    We give the solution of the functional equation f (x + y) + lambda f (x) f (y) = phi (x, y) under some conditions. Also we show its Hyers-Ulam stability. (c) 2006 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jmaa.2006.07.030

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  • Prime ideals and complex ring homomorphisms on a commutative algebra Reviewed

    Takeshi Miura, Sin-Ei Takahasi, Norio Niwa

    PUBLICATIONES MATHEMATICAE-DEBRECEN   70 ( 3-4 )   453 - 460   2007.4

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    eWe give a characterization of prime ideals P of a commutative complex algebra A in order that P be the kernel of some complex ring homomorphism on A. If, in addition, A is a uniform algebra on an infinite compact metric space, then we show that there are exactly 2' complex ring homomorphisms on A, whose kernels are non-maximal prime ideals. Moreover, it turns out that ring homomorphisms on a commutative Banach algebra are deeply connected with the existence of discontinuous homomorphisms.

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  • Unital and multiplicatively spectrum-preserving surjections between semi-simple commutative Banach algebras are linear and multiplicative Reviewed

    Osamu Hatori, Takeshi Miura, Hiroyuki Takagi

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   326 ( 1 )   281 - 296   2007.2

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    Let T be a surjective map from a unital semi-simple commutative Banach algebra A onto a unital commutative Banach algebra B. Suppose that T preserves the unit element and the spectrum sigma (fg) of the product of any two elements f and g in A coincides with the spectrum sigma (TfTg). Then B is semi-simple and T is an isomorphism. The condition that T is surjective is essential: An example of a non-linear and non-multiplicative unital map from a commutative C*-algebra into itself such that a (TfTg) = a (fg) holds for every f, g are given. We also show an example of a surjective unital map from a commutative C*-algebra onto itself which is neither linear nor multiplicative such that or (TfTg) subset of sigma (fg) holds for every f, g. (c) 2006 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jmaa.2006.02.084

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  • On the existence of continuous (approximate) roots of algebraic equations Reviewed

    Kazuhiro Kawamura, Takeshi Miura

    TOPOLOGY AND ITS APPLICATIONS   154 ( 2 )   434 - 442   2007.1

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    The present paper considers the existence of continuous roots of algebraic equations with coefficients being continuous functions defined on compact Hausdorff spaces. For a compact Hausdorff space X, C(X) denotes the Banach algebra of all continuous complex-valued functions on X with the sup norm parallel to.parallel to(infinity). The algebra C(X) is said to be algebraically closed if each monic algebraic equation with C(X) coefficients has a root in C(X). First we study a topological characterization of a first-countable compact (connected) Hausdorff space X such that C(X) is algebraically closed. The result has been obtained by Countryman Jr, Hatori-Miura and Miura-Niijima and we provide a simple proof for metrizable spaces.
    Also we consider continuous approximate roots of the equation z" - f = 0 with respect to z, where f is an element of C(X), and provide a topological characterization of compact Hausdorff space X with dim X <= 1 such that the above equation has an approximate root in C(X) for each f is an element of C(X), in terms of the first tech cohomology of X. (C) 2006 Elsevier B.V. All rights reserved.

    DOI: 10.1016/j.topol.2006.05.008

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  • Spectra preserving maps between commutative Banach algebras Reviewed

    O. Hatori, T. Miura, H. Takagi

    J. Math. Anal. Appl.   326   281 - 296   2007.1

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  • Remarks on n-th root closedness for commutative C*-algebras Reviewed

    D. Honma, T. Miura

    Nihonkai Math. J.   18   51 - 55   2007.1

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  • A survey of certain algebraic equations in commutative C*-algebras Reviewed

    T. Miura, D. Honma

    Contemp. Math.   435   327 - 333   2007.1

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  • Prime ideals and complex ring homomorphisms on a commutative Banach algebra Reviewed

    T. Miura, S.-E. Takahasi, N. Niwa

    Publ. Math. Debrecen   70   453 - 460   2007.1

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  • SUPERSTABILITY OF MULTIPLIERS AND RING DERIVATIONS ON BANACH ALGEBRAS Reviewed

    Takeshi Miura, Hirokazu Oka, Go Hirasawa, Sin-Ei Takahasi

    BANACH JOURNAL OF MATHEMATICAL ANALYSIS   1 ( 1 )   125 - 130   2007

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    In this paper, we will consider Hyers-Ulam-Rassias stability of multipliers and ring derivations between Banach algebras. As a corollary, we will prove superstability of ring derivations and multipliers. That is, approximate multipliers and approximate ring derivations are exact multipliers and ring derivations.

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  • On a characterization of compact hausdorff space xfor which certain algebraic equations are solvable in c(x) Reviewed

    Dai Honma, Takeshi Miura

    Tokyo Journal of Mathematics   30 ( 2 )   403 - 416   2007

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    Let X be a compact Hausdorff space and C(X) the Banach algebra of all complex-valued continuous functions on X. We consider the following property of C(X): for each f ∈ C(X) there exist a g ∈ C(X) and positive integers p and q such that p does not divide q and fq = gp. When X is locally connected, we give a necessary and sufficient condition for C(X) to have this property. We also give a characterization of a first-countable compact Hausdorff space X for which C(X) has the property above. As a corollary, we prove that if X is locally connected, or first-countable, then C(X) has the property above if and only if C(X) is algebraically closed. © 2007 International Academic Printing Co. Ltd. All rights reserved.

    DOI: 10.3836/tjm/1202136685

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  • On Wirtinger's inequality and its elementary proof Reviewed

    Sin-Ei Takahasi, Takeshi Miura, Takahiro Hayata

    Mathematical Inequalities and Applications   10 ( 2 )   311 - 319   2007

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    By an elementary method, we exactly determine the best possible constant and its attaining function which satisfy ∥f∥q ≤ C q∥f′∥q (1 &lt
    q &lt
    ∝) for certain class of continuously differentiable functions on the unit interval [0.1]. © ELEMENT.

    DOI: 10.7153/mia-10-27

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  • A perturbation of ring derivations on Banach algebras Reviewed

    Takeshi Miura, Go Hirasawa, Sin-Ei Takahasi

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   319 ( 2 )   522 - 530   2006.7

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    Suppose A is a Banach algebra and suppose f : A -> A is an approximate ring derivation in the sense of Hyers-Ulam-Rassias. This stability phenomenon was introduced for the first time in the subject of functional equations by Th.M. Rassias [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300]. If A has an approximate identity, or if A is semisimple and commutative, then we prove that f is an exact ring derivation. (c) 2005 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jmaa.2005.06.060

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  • On the first homology of the group of equivariant Lipschitz homeomorphisms Reviewed

    Kojun Abe, Kazuhiko Fukui, Takeshi Miura

    JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN   58 ( 1 )   1 - 15   2006.1

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    We study the structure of the group of equivariant Lipschitz homeomorphisms of a smooth G-manifold M which are isotopic to the identity through equivariant Lipschitz homeomorphisms with compact support. First we show that the group is perfect when M is a smooth free G-manifold. Secondly in the case of C-n with the canonical U(n)-action, we show that the first homology group admits continuous moduli. Thirdly we apply the result to the case of the group L(C, 0) of Lipschitz homeomorphisms of C fixing the origin.

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  • A reconsideration of Hua's inequality. Part II Reviewed

    Hiroyuki Takagi, Takeshi Miura, Takahiro Hayata, Sin-ei Takahasi

    JOURNAL OF INEQUALITIES AND APPLICATIONS   2006 ( Art. ID 21540 )   1 - 15   2006

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    We give a new interpretation of Hua's inequality and its generalization. From this interpretation, we know the best possibility of those inequalities.

    DOI: 10.1155/JIA/2006/21540

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  • Continuously differentiable means

    Jun Ichi Fujii, Masatoshi Fujii, Takeshi Miura, Hiroyuki Takagi, Sin-Ei Takahasi

    JOURNAL OF INEQUALITIES AND APPLICATIONS   Art. ID 75941   1 - 15   2006

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    We consider continuously differentiable means, say C-1-means. As for quasi-arithmetic means Q(f)(x(1),...,x(n)), we need an assumption that f has no stationary points so that Q(f) might be continuously differentiable. Introducing quasi-weights for C-1-means would give a satisfactory explanation for the necessity of this assumption. As a typical example of a class of C-1-means, we observe that a skew power mean M-t is a composition of power means if t is an integer. Copyright (C) 2006 Jun Ichi Fujii et al.

    DOI: 10.1155/JIA/2006/75941

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  • Hyers-Ulam stability of a closed operator in a Hilbert space Reviewed

    Go Hirasawa, Takeshi Miura

    Bulletin of the Korean Mathematical Society   43 ( 1 )   107 - 117   2006

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    We give some necessary and sufficient conditions in order that a closed operator in a Hilbert space into another have the Hyers-Ulam stability. Moreover, we prove the existence of the stability constant for a closed operator. We also determine the stability constant in terms of the lower bound.

    DOI: 10.4134/BKMS.2006.43.1.107

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  • Characterizations of isometric isomorphisms between uniform algebras via nonlinear range-preserving properties Reviewed

    O Hatori, T Miura, H Takagi

    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY   134 ( 10 )   2923 - 2930   2006

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    Let T be a surjective mapping from a uniform algebra A on a compact Hausdor. space X onto a uniform algebra on a compact Hausdor. space Y. Suppose that fg(X) = T(f)T(g)(Y) holds for every f, g is an element of A. Then we have that T is an almost isometric isomorphism, which is a generalization of results of Molnar (2002) and Rao and Roy (2005).

    DOI: 10.1090/S0002-9939-06-08500-5

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  • Convergency of a recursive sequence Xn+1 = βXn-1/ {1 + α(Xn-1 + Xn)} and its application to a model for competing species Reviewed

    Y. Miura, S.-E. Takahasi, T. Miura, M. Tsukada

    J. Anal. Appl.   3   205 - 222   2005.1

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  • Averaging functions and inequalities due to Holder-Rogers and Minkowski Reviewed

    S.-E. Takahasi, T. Miura, K. Sato

    Sci. Math. Jpn.   62   289 - 298   2005.1

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  • A reconsideration of Hua's inequality Reviewed

    Hiroyuki Takagi, Takeshi Miura, Tadashi Kanzo, Sin-Ei Takahasi

    JOURNAL OF INEQUALITIES AND APPLICATIONS   2005:1 ( 1 )   15 - 23   2005

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    The inequality discovered by L. K. Hua in 1965 has been generalized in several directions. In this paper, we adopt a certain conjugate method to give a simple and fundamental inequality on two functions on a semigroup, which is the key to the proof of many generalizations of Hua's inequality.

    DOI: 10.1155/JIA.2005.15

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  • Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras Reviewed

    Takeshi Miura, Sin-Ei Takahasi, Go Hirasawa

    JOURNAL OF INEQUALITIES AND APPLICATIONS   ( 4 )   2005

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    We prove that a Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra is a ring homomorphism. Using a signum effectively, we can give a simple proof of the Hyers-Ulam-Rassias stability of a Jordan homomorphism between Banach algebras. As a direct corollary, we show that to each approximate Jordan homomorphism f from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique ring homomorphism near to f.

    DOI: 10.1155/JIA.2005.435

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  • Stability of multipliers on Banach algebras Reviewed

    Takeshi Miura, Go Hirasawa, Sin-Ei Takahasi

    Int. J. Math. Math. Sci.   45   2377 - 2381   2004.10

  • A note on the Pearce-Pecaric inequalities Reviewed

    H. Takagi, T. Miura, S.-E. Takahasi

    Sci. Math. Jpn.   61   99 - 107   2004.10

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  • On the best constant of Hyers-Ulam stability Reviewed

    O. Hatori, K. Kobayashi, H. Takagi, T. Miura, S.-E. Takahasi

    J. Nonlinear Convex Anal.   5   387 - 393   2004.10

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  • The Hyers-Ulam stability constants of first order linear differential operators Reviewed

    SE Takahasi, H Takagi, T Miura, S Miyajima

    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS   296 ( 2 )   403 - 409   2004.8

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    Let X be a complex Banach space, h a complex-valued continuous function on the real line R and T-h : C-1 (R, X) --> C(R, X) the linear differential operator defined by T(h)u = u' + hu. We completely determine the Hyers-Ulam stability constant of Th. (C) 2004 Elsevier Inc. All rights reserved.

    DOI: 10.1016/j.jmaa.2003.12.044

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  • On convergency of a recursive sequence Xn+1 = f(Xn-1,Xn) Reviewed

    S.-E. Takahasi, Y. Miura, T. Miura

    Taiwanese J. Math.   10   631 - 638   2004.5

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  • Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras

    T. Miura, G. Hirasawa, S.-E. Takahasi

    J. Inequal. Appl.   2005:4   435 - 441   2004.2

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  • A note on commutative Gelfand theory for real Banach algebras Reviewed

    S.-E. Takahasi, T. Miura, O. Hatori

    J. Okayama Univ.   46   121 - 129   2004.1

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  • Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations y′ = λy

    Takeshi Miura, Soon-Mo Jung, Sin-Ei Takahasi

    Journal of the Korean Mathematical Society   41 ( 6 )   995 - 1005   2004

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    The aim of this paper is to prove the stability in the sense of Hyers-Ulam-Rassias of the Banach space valued differential equation y′ = λy, where λ is a complex constant. That is, suppose f is a Banach space valued strongly differentiable function on an open interval. If f is an approximate solution of the equation y′ = λy, then there exists an exact solution of the equation near to f.

    DOI: 10.4134/JKMS.2004.41.6.995

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  • On a characterization of the maximal ideal spaces of algebraically closed commutative C*-algebras Reviewed

    Takeshi Miura, Kazuki Niijima

    Proceedings of the American Mathematical Society   131 ( 9 )   2869 - 2876   2003.9

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    Let C(X) be the algebra of all complex-valued continuous functions on a compact Hausdorff space X. We say that C(X) is algebraically closed if each monic polynomial equation over C(X) has a continuous solution. We give a necessary and sufficient condition for C(X) to be algebraically closed for a locally connected compact Hausdorff space X. In this case, it is proved that C(X) is algebraically closed if each element of C(X) is the square of another. We also give a characterization of a first-countable compact Hausdorff space X such that C(X) is algebraically closed.

    DOI: 10.1090/S0002-9939-02-06835-1

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  • A characterization of Hyers-Ulam stability of first order linear differential operator. Reviewed

    T. Miura, S. Miyajima, S.-E. Takahasi

    J. Math. Anal. Appl. 286, 136--146   2003.6

  • Essential norm and stability constant for weighted composition operators on C(X). Reviewed

    H. Takagi, T. Miura, S.-E. Takahasi

    Bull. Korean Math. Soc. 40, 583--591.   2003.5

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  • Ring homomorphisms on real Banach algebras Reviewed

    Takeshi Miura, Sin-El Takahasi

    International Journal of Mathematics and Mathematical Sciences   2003 ( 48 )   3025 - 3029   2003

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    Let B be a strictly real commutative real Banach algebra with the carrier space φB. If A is a commutative real Banach algebra, then we give a representation of a ring homomorphism p:A→B, which needs not be linear nor continuous. If A is a commutative complex Banach algebra, then p (A) is contained in the radical of B. © 2003 Hindawi Publishing Corporation. All rights reserved.

    DOI: 10.1155/S0161171203302352

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  • Characterizations and automatic linearity for ring homomorphisms on algebras of functions. Reviewed

    O. Hatori, T. Ishii, T. Miura, S.-E. Takahasi

    Contep. Math. 328, 201--215.   2002.12

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  • A note on Wirtinger-Beesack's integral inequalities. Reviewed

    S.-E. Takahasi, T. Miura

    Math. Inequal. Appl. 6, 277--282.   2002.12

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  • On the structure of a third kind boundary value problem. Reviewed

    S.-E. Takahasi, H. Oka, T. Miura

    Math. Nachr. 257, 99--107.   2002.12

  • A representation of ring homomorphisms on unital regular commutative Banach algebras. Reviewed

    T. Miura

    Math, J. Okayama Univ. 44, 143--153.   2002.12

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  • Hyers-Ulam stability of linear differential operator with constant cofficients. Reviewed

    T. Miura, S. Miyajima, S.-E. Takahasi

    Math. Nachr. 258, 90--96.   2002.12

  • On the Hyers-Ulam stability of a differentiable map Reviewed

    T.Miura

    Sci. Math. Jpn., 55   2002.9

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  • On the Hyers-Ulam stability of the Banach space-valued differential equation y' = λy Reviewed

    S.-E. Takahasi, T. Miura, S. Miyajima

    Bull. Korean Math. Soc., 39   2002.9

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  • Polynomial identities that imply commutativity for rings Reviewed

    H. Takagi, S.-E. Takahasi, T. Miura

    Linear Algebra Appl. 341, 299-307.   2002.9

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  • A note on a class of Banach algebra-valued polynomials Reviewed

    Sin-Ei Takahasi, Osamu Hatori, Keiichi Watanabe, Takeshi Miura

    International Journal of Mathematics and Mathematical Sciences   32 ( 3 )   189 - 192   2002

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    Let F be a Banach algebra. We give a necessary and sufficient condition for F to be finite dimensional, in terms of finite type n-homogeneous F-valued polynomials. © 2002 Hindawi Publishing Corporation. All rights reserved.

    DOI: 10.1155/S0161171202203348

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  • Star ring homomorphism between commutative Banach algebras Reviewed

    Takeshi Miura

    Proc. Amer. Math. Soc. 129, 2005--2010.   2001.9

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  • A representation of ring homomorphisms on commutative Banach algebras Reviewed

    T. Miura

    Sci. Math. Jpn. 53, 515--523.   2001.9

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  • On the Hyers-Ulam stability of real continuous function valued differentiable map Reviewed

    T. Miura, S.-E. Takahasi, H. Choda

    Tokyo J. Math. 24, 467--476.   2001.9

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  • On a characterization of the maximal ideal spaces of commutative C*-algebras in which every element is the square of another Reviewed

    O. Hatori, T. Miura

    Proc. Amer. Math. Soc. 128, 1185--1189.   2000.1

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  • On commutative C*-algebras in which every element is almost the square of another Reviewed

    Takeshi Miura

    Contemp. Math.   232   289 - 242   1999.1

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Books

  • 複素関数への一歩

    学術図書出版社  2010.9 

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  • 線型代数の発想

    学術図書出版社  2006.10 

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MISC

  • A note on the stability of an integral equation (accepted)

    T. Miura, G. Hirasawa, S.-E. Takahasi, T. Hayata

    Functional equations in mathematical analysis   2011.1

  • On the Butler-Rassias functional equation and its generalized Hyers-Ulam stability (accepted)

    T. Miura, G. Hirasawa, T. Hayata

    Functional Equations in Mathematical Analysis   2010.11

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  • Approximate unitaries in B(H)

    M. Mirzavaziri, T. Miura, M. Moslehian

    East Journal of Approximations   2010.11

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  • The Hyers-Ulam and Ger type stabilities of the first order linear differential equations (accepted)

    T. Miura, G. Hirasawa

    Functional Equations in Mathematical Analysis   2010.11

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  • A note on the stability of an integral equation (accepted)

    T. Miura, G. Hirasawa, S.-E. Takahasi, T. Hayata

    Functional Equations in Mathematical Analysis   2010.11

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  • Ger-type stability of the first order linear differential equation for holomorphic functions Reviewed

    T. Miura

    Nonlinear Funct. Anal. Appl.   2010.4

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  • Effect of Charge Transfer Complex on Electrical Properties of 4-Cyano-4 '-pentylbiphenyl

    Tomonori Koda, Toshihiro Mitsuyoshi, Akihiko Kanazawa, Akihiro Nishioka, Ken Miyata, Go Murasawa, Susumu Ikeda, Takeshi Miura, Yasuyuki Kimura

    JAPANESE JOURNAL OF APPLIED PHYSICS   48 ( 12 )   2009.12

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    Language:English   Publisher:JAPAN SOC APPLIED PHYSICS  

    The dielectric constant, threshold voltage, and response time were measured for a nematic binary mixture of 4-cyano-4'-pentylbiphenyl (5CB) molecules and the doped electron acceptor tetracyanoethylene (TCNE). The doping of TCNE caused a large increase in the dielectric constant and dielectric anisotropy. However, no marked improvement was achieved for threshold voltage and response time. Considering that the large increase was due to mobile charges in the system, we proposed a theoretical model to discuss the singularity that appeared in experimental results obtained in an electric field. (C) 2009 The Japan Society of Applied Physics

    DOI: 10.1143/JJAP.48.121404

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  • Ger type stability of the first order linear differential equation y'(t) = h(t)y(t)

    T. Miura, H. Oka, S.-E. Takahasi, N. Niwa

    Tamsui Oxf. J. Math. Sci.   24   445 - 456   2008.12

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  • A perturbation of normal operators on a Hilbert space

    T. Miura, A. Uchiyama, H. Oka, G. Hirasawa, S.-E. Takahasi, N. Niwa

    Nonlinear Funct. Anal. Appl.   13   291 - 297   2008.9

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  • On solvability of certain algebraic equations in commutative C*-algebras

    三浦 毅, 本間 大

    北海道大学数学講究録   119   2007.4

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  • Hyers-Ulam stability problem and Cauchy-Euler type factorization

    髙橋 眞映, 岡 裕和, 三浦 毅, 髙木 啓行

    北海道大学数学講究録   119   2007.4

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  • 関数と確率測度の可換の度合いをはかる評価

    髙橋 眞映, 三浦 毅, 早田 孝博

    実解析学シンポジウム報告集   2006.4

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  • 2つの可換Banach環の間のスペクトル保存写像,Ⅰ

    高木 啓行, 羽鳥 理, 三浦 毅

    北海道大学数学講究録   105   2006.4

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  • 2つの可換Banach環の間のスペクトル保存写像,II

    羽鳥 理, 三浦 毅, 高木 啓行

    北海道大学数学講究録   105   2006.4

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  • 平均考,II

    髙橋 眞映, 高木 啓行, 三浦 毅, 藤井 淳一, 藤井 正俊

    北海道大学数学講究録   105   2006.4

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  • Note on the Hyers-Ulam-Rassias stability of the first order linear differential equation y'(t) + p(t)y(t) + q(t) = 0

    T. Miura, G. Hirasawa, S.-E. Takahasi

    Nonlinear Funct. Anal. Appl.   11   851 - 858   2006.1

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  • The Hyers-Ulam-Rassias stability of differential operators and its applications

    Takeshi Miura

    Nonlinear Funct. Anal. Appl.   10 ( 5 )   535 - 553   2004.10

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  • The Hyers-Ulam stability of a weighted composition operator on a uniform algebra

    三浦 毅, H. Takagi, T. Miura, S.-E. Takahasi

    J. Nonlinear Convex Anal. 5, 43--48.   2004.1

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  • Ger type and Hyers-Ulam stabilities for the first order linear differential operators of entire functions

    T. Miura, G. Hirasawa, S.-E. Takahasi

    Int. J. Math. Math. Sci. 22, 1151--1158.   2004.1

  • Prime ideals and complex ring homomorphisms

    三浦 毅

    北海道大学数学講究録   73   2003.4

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  • On the Hyers-Ulam stability constant

    髙橋 眞映, 三浦 毅, 宮島 静雄

    北海道大学数学講究録   73   2003.4

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  • On the Hyers-Ulam stability of a differentiable map,

    三浦 毅

    北海道大学数学講究録   66   2001.12

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  • Perturbations of $\ast$-ring homomorphisms on commutative Banach algebras

    Takeshi Miura

    Proceedings of International Workshop Operator Theory and Its Applications   1999.1

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    9999年04月

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Presentations

  • 関数環上の実線形等距離写像の構造

    関数環研究集会  2011 

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  • Function algebras上のisometries

    つくばセミナー  2011 

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  • Function spaces上のisometries

    つくばセミナー  2011 

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  • Real linear isometries between function algebras

    Reaserch on preserver problems concerning to Banach algebras and its applications  2011 

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  • 可換Banach環上の乗法的スペクトル保存写像

    日本数学会  2010 

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  • Spectrally additive surjections between uniform algebras

    Sattelite Seminar in Niigata of Takahasi International  2010 

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  • 乗法的複素数値関数を超安定にさせる2項演算の決定

    日本数学会  2010 

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  • Generalizations of spectrally multiplicative surjections between uniform algebras

    The Sixth Conference on Fucntion Spaces  2010 

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  • Banach-Stoneの定理とその拡張

    可換Banach環と種々の分野との交流II  2010 

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  • Peripherally multiplicative surjections between uniform algebras

    American Mathematical Society Sectional Meeting  2009 

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  • Standard operator algebra上のperipheral spectrum保存写像2

    関数環研究集会  2009 

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  • Standard operator algebra上のperipheral spectrum保存写像

    関数環研究集会  2008 

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  • A note on the stability of Volterra typw integral equation

    The Twelfth International Conference of Functional Equations and Inequalities  2008 

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  • 可換C*$-環上の代数方程式について

    日本数学会  2007 

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  • 作用素のCauchy-Euler型因数分解

    日本数学会  2007 

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  • Banach環のunitization上のnormに関する話

    実解析学シンポジウム  2007 

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  • Hyers-Ulam stabilityの歴史

    米沢数学セミナー  2007 

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  • 可換C*-環に係数をもつある種の代数方程式の可解性と極大イデアル空間の位相構造

    実函数論・函数解析学合同シンポジウム  2007 

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  • 関数環上のある種の値域保存写像

    日本数学会  2007 

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  • 可換Banach環上のある種のノルムを保存する写像

    関数環研究集会  2006 

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  • C(X)上のある種の代数方程式とその可解性

    第15回関数空間セミナー  2006 

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  • L^p空間におけるHua型方程式

    日本数学会  2006 

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  • A generalization of Wang's inequality

    日本数学会  2006 

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  • On the maximal ideal spaces of commutative C*-algebras in which certain algebraic equation is solvable

    The Fifth Conference on Function Spaces  2006 

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  • C(K)空間上の等距離同型写像の特徴づけ

    第69回米沢数学セミナー  2006 

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  • Banach環上のring derivationとその摂動

    日本数学会  2006 

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  • Wirtingerの不等式とその初等的証明

    日本数学会  2006 

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  • 平均関数と不等式

    日本数学会  2005 

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  • A Hua type inequality of L^p-spaces

    実解析学シンポジウム2005  2005 

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  • 2つの可換Banach環の間のスペクトル保存写像I

    第14回関数空間セミナー  2005 

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  • 2つの可換Banach環の間のスペクトル保存写像II

    第14回関数空間セミナー  2005 

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  • Multiplierの摂動とその存在

    応用函数解析としての情報数理の研究  2005 

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  • Banach環上のmultiplierとその摂動

    日本数学会  2005 

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  • ものの考え方(Huaの不等式を例にとって)

    日本数学会  2005 

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  • Batler-Rassias型関数方程式とそのHyers-Ulam stability

    日本数学会  2005 

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  • Hua型不等式に関する注意

    日本数学会  2005 

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  • 複素多元環上の環準同型写像と素イデアル

    日本数学会  2005 

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  • 正則な可換Banach環の全射環準同型写像による像

    関数環研究集会  2004 

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  • Butler-Rassias type functional equation and its Hyers-Ulam stability

    第13回関数空間セミナー  2004 

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  • A way of thinking

    第13回関数空間セミナー  2004 

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  • A note on Hua-type inequalities

    第13回関数空間セミナー  2004 

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  • On convergency of a recursive sequence x_n+1 = x_n-N/ {(1 + x_n-N+1 x_n-N+2)x_n}

    International Symposium on Dynamical Systems  2004 

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  • C(X)上の代数方程式の解の存在性とXの位相構造

    情報科学と函数解析の接点  2004 

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  • Huaの不等式に関するPeace-Pecaricの論文への注意

    情報科学と函数解析の接点  2004 

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  • Huaの不等式再考

    日本数学会  2004 

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  • multiplierの摂動とその安定性

    第62回米沢数学セミナー  2004 

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  • 線形微分作用素のある種の安定性

    実函数論・函数解析学合同シンポジウム  2004 

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  • 平方根に関連する話題

    第2回関数環若手セミナー  2004 

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  • 亜距離空間上の鏡映とMazur-Ulam's Theorem

    非線形解析学と凸解析学の研究  2004 

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  • 差分方程式x_n+1 = f(x_n-1,x_n)の解の収束性と種の競合問題

    日本数学会  2004 

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  • 可換Banach環上のJordan homomorphismとその安定性

    非線形解析学と凸解析学の研究  2003 

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  • 任意の代数方程式が解をもつ可換C*-環の極大イデアル空間による特徴づけ

    日本数学会  2003 

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  • 関数環上の荷重合成作用素のHyers-Ulam stability

    日本数学会  2003 

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  • 差分方程式x_n+1 = f(x_n-1, x_n)の解の収束性

    日本数学会  2003 

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  • 線形微分作用素の安定性についての2,3の注意

    実解析学シンポジウム2003  2003 

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  • Huaの不等式再考

    実解析学シンポジウム2003  2003 

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  • Banach環上のJordan準同型写像の摂動とその安定性

    関数環研究集会  2003 

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  • 線形作用素とその安定性

    第12回関数空間セミナー  2003 

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  • 一階定数係数線型微分作用素のHyers-Ulam stability

    第12回関数空間セミナー  2003 

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  • 関数環上のどんな荷重合成作用素がHyers-Ulam stabilityを満たすか?

    第12回関数空間セミナー  2003 

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  • 半可換性と不等式

    第12回関数空間セミナー  2003 

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  • 数列x_n+1 = x_n-1/ (1 + x_n)の面白さと関連する話題

    情報科学としての函数解析とその周辺  2003 

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  • 楕円型微分方程式の解集合の構造

    日本数学会  2003 

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  • 1階線形微分作用素のHyers-Ulam stability

    日本数学会  2003 

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  • 環準同型写像の摂動とその安定性

    第59回米沢数学セミナー  2003 

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  • A Hua type inequality on semigroup

    International Symposium of Operator Theory  2003 

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  • On Wirtinger-Beesack type integral inequalitie

    The Third International Conference on Nonlinear Analysis and Convex Analysis  2003 

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  • 可換Banach環上の環準同型写像

    解析関数とその周辺  2003 

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  • 線形微分作用素のHyers-Ulam stability

    実解析学シンポジウム2002  2002 

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  • 1階線形微分作用素のHyers-Ulam stabilityについて

    第11回関数空間セミナー  2002 

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  • 与えられた素イデアルを核とする複素環準同型写像の存在性

    第11回関数空間セミナー  2002 

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  • C上のU(1)-同変リプシッツ同相群の1次元ホモロジー群

    新しい観点からみた変換群論  2002 

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  • 任意の代数方程式が可解となる可換C*-環の極大イデアル空間

    早稲田大学7階セミナー  2002 

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  • 複素数体上の不連続な準同型写像

    第55回米沢数学セミナー  2002 

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  • C(X)上の荷重合成作用素に関するいくつかの量について

    非線形解析学と凸解析学の研究  2002 

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  • 定数係数線形微分作用素のHyers-Ulam stability

    日本数学解  2002 

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  • Wirtinger型不等式に関する一考察

    函数解析学と数理情報の接点  2001 

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  • 楕円型微分方程式の解集合について

    非線形解析学と凸解析学の研究  2001 

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  • 任意の代数方程式が解をもつ可換C*-環の極大イデアル空間

    調和・解析関数空間と線形作用素II  2001 

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  • 可換C*-環上の環準同型写像

    第10回関数空間セミナー  2001 

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  • Hyers-Ulam stabilityと微分作用素のお話

    第10回関数空間セミナー  2001 

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  • 代数的に閉じた可換C*-環の極大イデアル空間

    第52回米沢数学セミナー  2001 

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  • 対合をもつ可換Banach環上の*-環準同型写像の摂動

    函数解析学と数理情報の接点  2001 

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  • On the Hyers-Ulam stability of a differentiable map

    第9回関数空間セミナー  2000 

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  • 数学を楽しもう

    第45回米沢数学セミナー  2000 

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  • C(X)上の環準同型写像について

    第46回米沢数学セミナー  2000 

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  • 可換Banach環上の環準同型写像について

    日本数学解  2000 

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  • 実連続関数に値をとる微分可能な写像のHyers-Ulam stabilityについて

    日本数学解  2000 

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  • 正則な可換Banach環上の環準同型写像

    関数環論とその応用研究集会  2000 

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  • Ring homomorphisms on commutative Banach algebras II

    解析関数空間とその上の作用素論  1999 

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  • Ring Homomorphisms from commutative Banach Algebras

    International Workshop Operator Theory and Its Applications  1999 

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  • 複素環準同型写像の核について

    第40回米沢数学セミナー  1999 

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  • 可換Banach環上の環準同型写像について

    実解析学サマーセミナー  1999 

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  • 二乗根をもつ可換C*-環の極大イデアル空間について

    日本数学会  1999 

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  • 実連続関数に値をとる微分可能な写像のHyers-Ulam stabilityについて

    非線形解析学と凸解析学の研究  1999 

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  • 可換Banach環上の*-環準同型についての2,3の注意

    関数環研究集会  1998 

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  • On Banach function algebras in which every element is square of another

    The Third Conference on Function Spaces  1998 

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  • C(X)上の準同型のperturbationについて(Semrlの仕事の紹介)

    第33回米沢数学セミナー  1998 

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  • 方程式x^2 = aが解をもつ可換C*-環の極大イデアル空間について

    関数環論研究集会  1997 

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  • 2次方程式が可解となる可換C*-環の極大イデアル空間の位相的性質

    第23回米沢数学セミナー  1997 

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Research Projects

  • 可換Banach環理論

    1999

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    Grant type:Competitive

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Teaching Experience

  • 先端科学技術総論

    2022
    Institution name:新潟大学

  • 数理解析特別講義

    2022
    Institution name:新潟大学

  • 理学スタディ・スキルズ

    2022
    Institution name:新潟大学

  • 微分積分学IIB

    2021
    Institution name:新潟大学

  • 微分積分学IIA

    2021
    Institution name:新潟大学

  • 領域概説 B (理学)

    2021
    Institution name:新潟大学

  • 数理解析特別講義

    2020
    Institution name:新潟大学

  • 関数空間特論

    2020
    Institution name:新潟大学

  • 解析学序論B

    2018
    -
    2020
    Institution name:新潟大学

  • 解析学序論A

    2018
    -
    2020
    Institution name:新潟大学

  • 理学スタディ・スキルズ

    2018
    -
    2020
    Institution name:新潟大学

  • 複素解析学IIB

    2017
    Institution name:新潟大学

  • 複素解析学IB

    2017
    Institution name:新潟大学

  • 複素解析学IA

    2017
    Institution name:新潟大学

  • 複素解析学IIA

    2017
    Institution name:新潟大学

  • 解析学基礎1

    2017
    -
    2020
    Institution name:新潟大学

  • 解析学基礎2

    2017
    -
    2020
    Institution name:新潟大学

  • 数学基礎演習a

    2017
    -
    2019
    Institution name:新潟大学

  • 数学基礎演習b

    2017
    -
    2019
    Institution name:新潟大学

  • 専門力アクティブ・ラーニング

    2017
    Institution name:新潟大学

  • 微分積分学III

    2015
    -
    2017
    Institution name:新潟大学

  • スタディ・スキルズ(数学・情報学習法)

    2015
    -
    2016
    Institution name:新潟大学

  • 数理物質科学特定研究Ⅰ(数学)

    2015
    Institution name:新潟大学

  • 数理科学文献詳読Ⅰ(数学)

    2015
    Institution name:新潟大学

  • 数理科学研究発表演習〔中間発表〕(数学)

    2015
    Institution name:新潟大学

  • 数理科学セミナーⅠ(数学)

    2015
    Institution name:新潟大学

  • Functional Analysis and its Applications

    2014
    Institution name:新潟大学

  • 複素解析学

    2013
    Institution name:新潟大学

  • 数学講究

    2013
    Institution name:新潟大学

  • 複素解析特論

    2013
    Institution name:新潟大学

  • 数学基礎A

    2013
    -
    2016
    Institution name:新潟大学

  • 複素解析学I

    2013
    -
    2016
    Institution name:新潟大学

  • 複素解析学II

    2013
    -
    2016
    Institution name:新潟大学

  • スタディ・スキルズ(数学学習法)

    2013
    -
    2014
    Institution name:新潟大学

  • 数学英語

    2013
    -
    2014
    Institution name:新潟大学

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