自然科学研究科 数理物質科学専攻 教授
理学部 理学科 教授
2025/04/02 更新
研究活動
教育活動
2025/04/02 更新
博士(理学) ( 2000年3月 新潟大学 )
可換Banach環論
スペクトル保存写像
Spectra preserving maps
Commutative Banach algebras
phase isometry
等距離写像
保存問題
自然科学一般 / 基礎解析学
新潟大学 自然系(理学部) 教授
2013年4月 - 現在
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Professor,Graduate School of Science and Engineering ,Yamagata University
2010年4月 - 現在
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山形大学 Graduate School of Science and Engineering
2010年4月 - 2013年3月
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Associate Professor,Graduate School of Science and Engineering ,Yamagata University
2007年4月 - 2010年3月
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山形大学 Graduate School of Science and Engineering
2007年4月 - 2010年3月
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Associate Professor,Faculty of Engineering,Yamagata University
2005年4月 - 2007年3月
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山形大学 Faculty of Engineering, Faculty of Engineering
2005年4月 - 2007年3月
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Associate Professor,International Student Center,Yamagata University
2005年4月 - 2006年3月
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山形大学留学生センター 助教授
2005年4月 - 2006年3月
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Associate Professor,International Student Center,Yamagata University
2003年4月 - 2005年3月
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山形大学留学生センター 助教授
2003年4月 - 2005年3月
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山形大学 Faculty of Engineering, Faculty of Engineering
2001年4月 - 2003年3月
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Lecturer,Faculty of Engineering,Yamagata University
2001年4月 - 2003年3月
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新潟大学 理学部 理学科 教授
2017年4月 - 現在
新潟大学 自然科学研究科 数理物質科学専攻 教授
2013年4月 - 現在
新潟大学 自然科学研究科 数理物質科学専攻 教授
2013年4月 - 現在
新潟大学 数理解析学 教授
2013年4月 - 2017年3月
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年4月 - 2009年3月
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Tingley’s problem for complex Banach spaces which do not satisfy the Hausdorff distance condition 査読
David Cabezas, María Cueto-Avellaneda, Yuta Enami, Takeshi Miura, Antonio M. Peralta
Banach Journal of Mathematical Analysis 17 ( 4 ) 2023年7月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:Springer Science and Business Media LLC
DOI: 10.1007/s43037-023-00291-0
その他リンク: https://link.springer.com/article/10.1007/s43037-023-00291-0/fulltext.html
Ordered continuous bands on the positive real numbers and distribution 査読
Hirokazu Oka, Takeshi Miura, Norio Niwa, Sin-Ei Takahasi
Publicationes Mathematicae Debrecen 102 ( 3-4 ) 507 - 524 2023年4月
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掲載種別:研究論文(学術雑誌) 出版者・発行元:University of Debrecen/ Debreceni Egyetem
Surjective isometries on a Banach space of analytic functions with bounded derivatives 査読
Takeshi Miura, Norio Niwa
Acta Scientiarum Mathematicarum 89 ( 1-2 ) 109 - 145 2023年3月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:Springer Science and Business Media LLC
DOI: 10.1007/s44146-023-00062-1
その他リンク: https://link.springer.com/article/10.1007/s44146-023-00062-1/fulltext.html
Tingley's problem for a Banach space of Lipschitz functions on the closed unit interval 査読
Daisuke Hirota, Takeshi Miura
RIMS Kokyuroku Bessatsu B93 157 - 181 2023年
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Surjective isometries on an algebra of analytic functions with C^n-boundary values 査読
Yuta Enami and Takeshi Miura
RIMS Kokyuroku Bessatsu B93 83 - 107 2023年
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Special noncancellative commutative semigroup operations on the real numbers and distribution 査読
T. Miura, N. Niwa, H. Oka, S.-E. Takahasi
Acta Mathematica Hungarica 168 ( 2 ) 363 - 372 2022年12月
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掲載種別:研究論文(学術雑誌) 出版者・発行元:Springer Science and Business Media LLC
DOI: 10.1007/s10474-022-01285-4
その他リンク: https://link.springer.com/article/10.1007/s10474-022-01285-4/fulltext.html
Every commutative JB$$^*$$-triple satisfies the complex Mazur–Ulam property 査読
David Cabezas, María Cueto-Avellaneda, Daisuke Hirota, Takeshi Miura, Antonio M. Peralta
Annals of Functional Analysis 13 ( 4 ) 2022年8月
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掲載種別:研究論文(学術雑誌) 出版者・発行元:Springer Science and Business Media LLC
Abstract
We prove that every commutative JB$$^*$$-triple, represented as a space of continuous functions$$C_0^{\mathbb {T } }(L),$$satisfies the complex Mazur–Ulam property, that is, every surjective isometry from the unit sphere of$$C_0^{\mathbb {T } }(L)$$onto the unit sphere of any complex Banach space admits an extension to a surjective real linear isometry between the spaces.
DOI: 10.1007/s43034-022-00204-6
その他リンク: https://link.springer.com/article/10.1007/s43034-022-00204-6/fulltext.html
Exploring new solutions to Tingley’s problem for function algebras 査読
María Cueto-Avellaneda, Daisuke Hirota, Takeshi Miura, Antonio M. Peralta
Quaestiones Mathematicae 46 ( 7 ) 1315 - 1346 2022年6月
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A Special Noncommutative Semigroup Operation on the Real Numbers and Left or Right Distribution 査読
Takeshi Miura, Norio Niwa, Hirokazu Oka, Sin-Ei Takahasi
Results in Mathematics 77 ( 2 ) 2022年1月
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掲載種別:研究論文(学術雑誌) 出版者・発行元:Springer Science and Business Media LLC
DOI: 10.1007/s00025-021-01588-y
その他リンク: https://link.springer.com/article/10.1007/s00025-021-01588-y/fulltext.html
Approximate local isometries of derivative Hardy spaces 査読
A. Jiménez-Vargas, Takeshi Miura
Quaestiones Mathematicae 46 ( 1 ) 23 - 34 2021年10月
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2-local real-linear isometries on <i>C</i><sup>(1)</sup>([0, 1])
Hironao Koshimizu, Takeshi Miura
Quaestiones Mathematicae 45 ( 9 ) 1353 - 1361 2021年7月
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Hirokazu Oka, Takeshi Miura, Sin-Ei Takahasi
Acta Scientiarum Mathematicarum 86 ( 3-4 ) 493 - 502 2020年12月
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掲載種別:研究論文(学術雑誌) 出版者・発行元:Springer Science and Business Media LLC
DOI: 10.14232/actasm-020-116-1
その他リンク: https://link.springer.com/article/10.14232/actasm-020-116-1/fulltext.html
Semigroup operations distributed by natural noncancellative semigroup operations on the positive real numbers 査読
H. Oka, T. Miura, S.-E. Takahasi
Semigroup Forum to appear 2020年
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Characterization of distributive semigroup operation onthe positive real numbers 査読
S.-E. Takahasi, T. Miura, H. Oka
Semigroup Forum 2020年
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Classification of semisimple commutative Banach algebras of type I 査読
J. Inoue, T. Miura, H. Takagi, S.-E. Takahasi
Nihonkai Math. J 30 1 - 17 2019年
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2-local isometries on C^(n)([0,1]) 査読
K. Kawamura, H. Koshimizu, T. Miura
Contemp. Math. 737 119 - 124 2019年
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Corrigendum to ``Examples of generalized bi-circular idempotnts on spaces of continuously differentiable functions" 査読
F. Botelho, T. Miura
J. Math. Anal. Appl. 474 1481 - 1487 2019年
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Examples of generalized bi-circular idempotents on spaces of continuously differentiable functions 査読
Fernanda Botelho, Takeshi Miura
Journal of Mathematical Analysis and Applications 465 ( 2 ) 795 - 802 2018年9月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元: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.
Surjective isometries on a Banach space of analytic functions on the open unit disc 査読
T. Miura, N. Niwa
Nihonkai Math. J. 29 51 - 65 2018年
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Norms on C1([0, 1]) and their isometries 査読
Kazuhiro Kawamura, Hironao Koshimizu, Takeshi Miura
Acta Scientiarum Mathematicarum 84 ( 1-2 ) 239 - 261 2018年
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記述言語:英語 掲載種別:研究論文(国際会議プロシーディングス) 出版者・発行元: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]).
Real-linear surjective isometries between function spaces 査読
Kazuhiro Kawamura, Takeshi Miura
TOPOLOGY AND ITS APPLICATIONS 226 66 - 85 2017年8月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元: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.
Surjective isometries on the banach space of continuously differentiable functions 査読
Takeshi Miura, Hiroyuki Takagi
Contemporary Mathematics 687 181 - 192 2017年
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記述言語:英語 掲載種別:論文集(書籍)内論文 出版者・発行元:American Mathematical Society
Let C1 [0, 1] be the Banach space of all continuously differentiable complex valued functions on the unit interval [0, 1] with the norm ‖f‖Σ = ‖f‖∞ + ‖f′ ‖∞ for f ∈ C1 [0, 1]. We give a characterization of surjective, not necessarily linear, isometries on C1 [0, 1]. This is a generalization of a result by Rao and Roy that describes surjective complex linear isometries on C1 [0, 1].
Semigroup operations distributed by the ordinary multiplication or addition on the real numbers 査読
Sin-Ei Takahasi, Hiroyuki Takagi, Takeshi Miura, Hirokazu Oka
PUBLICATIONES MATHEMATICAE-DEBRECEN 91 ( 3-4 ) 297 - 307 2017年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:KOSSUTH LAJOS TUDOMANYEGYETEM
We characterize the cancellative and continuous semigroup operations on the real field which are distributed by the ordinary multiplication or addition.
A Characterization of Multipliers of a Lau Algebra Constructed by Semisimple Commutative Banach Algebras 査読
Sin-Ei Takahasi, Hiroyuki Takagi, Takeshi Miura
TAIWANESE JOURNAL OF MATHEMATICS 20 ( 6 ) 1401 - 1415 2016年12月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元: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.
Mappings onto multiplicative subsets of function algebras and spectral properties of their products 査読
Takeshi Miura, Thomas Tonev
ARKIV FOR MATEMATIK 53 ( 2 ) 329 - 358 2015年10月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元: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.
Surjective isometries between function spaces 査読
Takeshi Miura
FUNCTION SPACES IN ANALYSIS 645 231 - 239 2015年
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記述言語:英語 掲載種別:研究論文(国際会議プロシーディングス) 出版者・発行元: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.
Ulam type stability problems for alternative homomorphisms 査読
Sin-Ei Takahasi, Makoto Tsukada, Takeshi Miura, Hiroyuki Takagi, Kotaro Tanahashi
JOURNAL OF INEQUALITIES AND APPLICATIONS 2014年6月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元: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.
Real-linear isometries between subspaces of continuous functions 査読
Hironao Koshimizu, Takeshi Miura, Hiroyuki Takagi, Sin-Ei Takahasi
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 413 ( 1 ) 229 - 241 2014年5月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元: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.
Real linear isometries between function algebras. II 査読
Osamu Hatori, Takeshi Miura
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS 11 ( 10 ) 1838 - 1842 2013年10月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:VERSITA
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.
A CHARACTERIZATION OF THE STABILITY OF A SYSTEM OF THE BANACH SPACE VALUED DIFFERENTIAL EQUATIONS 査読
Takeshi Miura, Go Hirasawa, Sin-Ei Takahasi, Takahiro Hayata
MATHEMATICAL INEQUALITIES & APPLICATIONS 16 ( 3 ) 717 - 728 2013年7月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元: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
Isometries and maps compatible with inverted Jordan triple products on groups 査読
Osamu Hatori, Go Hirasawa, Takeshi Miura, Lajos Molnár
Tokyo Journal of Mathematics 35 ( 2 ) 385 - 410 2012年12月
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記述言語:英語 掲載種別:研究論文(学術雑誌)
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.
Stability of the Banach space valued Chebyshev differential equation 査読
Takeshi Miura, Sin-Ei Takahasi, Takahiro Hayata, Kotaro Tanahashi
APPLIED MATHEMATICS LETTERS 25 ( 11 ) 1976 - 1979 2012年11月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:PERGAMON-ELSEVIER SCIENCE LTD
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.
Real-linear isometries between function algebras
Takeshi Miura
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS 9 ( 4 ) 778 - 788 2011年8月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:VERSITA
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.
Spectral radii conditions for isomorphisms between unital semisimple commutative Banach algebras 査読
Go Hirasawa, Takeshi Miura, Hiroyuki Takagi
FUNCTION SPACES IN MODERN ANALYSIS 547 125 - 134 2011年
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記述言語:英語 掲載種別:研究論文(国際会議プロシーディングス) 出版者・発行元:AMER MATHEMATICAL SOC
Let I be an index set and let A and B be unital semisimple commutative Banach algebras with maximal ideal spaces MA and M(B), respectively. If surjective maps S(k): I -> A and T(k) : I -> B satisfy r(S(1)(lambda)S(2)(mu) - e) = r(T(1)(lambda)T(2)(mu) - e) for all lambda, mu is an element of I, then there exist u(k) is an element of B(-1), a homeomorphism phi: M(B) -> M(A) and a clopen subset K subset of M(B) such that u(k)(-1)T(k)(lambda) = S(k)(lambda) circle phi on K and u(k)(-1)T(k)(lambda) = <(S(k)(lambda) circle phi)over bar> on M(B) \ K for all lambda is an element of I and k = 1,2. Here, r(.) is the spectral radius of algebra elements.
An equality condition of Arhippainen-Müller's estimate and its related problem 査読
Sin-Ei Takahasi, Takeshi Miura, Takahiro Hayata
Taiwanese Journal of Mathematics 15 ( 1 ) 165 - 169 2011年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元: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.
Divisibly norm-preserving maps between commutative banach algebras 査読
Takeshi Miura, Dai Honma, Rumi Shindo
Rocky Mountain Journal of Mathematics 41 ( 5 ) 1675 - 1699 2011年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:Rocky Mountain Mathematics Consortium
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.
Spectral Preservers in Commutative Banach Algebras 査読
Osamu Hatori, Scott Lambert, Aaron Luttman, Takeshi Miura, Thomas Tonev, Rebekah Yates
FUNCTION SPACES IN MODERN ANALYSIS 547 103 - + 2011年
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記述言語:英語 掲載種別:研究論文(国際会議プロシーディングス) 出版者・発行元:AMER MATHEMATICAL SOC
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.
Generalizations of spectrally multiplicative surjections between uniform algebras 査読
Osamu Hatori, Takeshi Miura, Rumi Shindo, Hiroyuki Takagi
Rendiconti del Circolo Matematico di Palermo 59 ( 2 ) 161 - 183 2010年8月
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記述言語:英語 掲載種別:研究論文(学術雑誌)
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.
Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras 査読
Osamu Hatori, Go Hirasawa, Takeshi Miura
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS 8 ( 3 ) 597 - 601 2010年6月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:VERSITA
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.
ON A HYERS-ULAM-AOKI-RASSIAS TYPE STABILITY AND A FIXED POINT THEOREM 査読
Sin-Ei Takahasi, T. Miura, H. Takagi
JOURNAL OF NONLINEAR AND CONVEX ANALYSIS 11 ( 3 ) 423 - 439 2010年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元: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.
A generalization of peripherally-multiplicative surjections between standard operator algebras 査読
Takeshi Miura, Dai Honma
CENTRAL EUROPEAN JOURNAL OF MATHEMATICS 7 ( 3 ) 479 - 486 2009年9月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:VERSITA
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.
Peripherally Monomial-Preserving Maps between Uniform Algebras 査読
Osamu Hatori, Kazumi Hino, Takeshi Miura, Hirokazu Oka
MEDITERRANEAN JOURNAL OF MATHEMATICS 6 ( 1 ) 47 - 59 2009年3月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元: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.
An estimate of the commutativity of $C^2$-function and probability measure 査読
T. Miura, T. Hayata, S.-E. Takahasi
J. Math. Inequal. 3 169 - 180 2009年1月
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Stability of almost multiplicative functionals 査読
N. Niwa, H. Oka, T. Miura, S.-E. Takahasi
Aust. J. Math. Anal. Appl. 9 1 - 8 2009年1月
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Reflections and a generalization of the Mazur-Ulam theorem (accepted) 査読
O. Hatori, K. Kobayashi, T. Miura, S.-E. Takahasi
Rocky Mountain J. Math. 2009年1月
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On the root closedness of continuous function algebras 査読
Kazuhiro Kawamura, Takeshi Miura
TOPOLOGY AND ITS APPLICATIONS 156 ( 3 ) 624 - 628 2009年1月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元: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.
Superstability of Generalized Multiplicative Functionals 査読
Takeshi Miura, Hiroyuki Takagi, Makoto Tsukada, Sin-Ei Takahasi
JOURNAL OF INEQUALITIES AND APPLICATIONS 2009年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:HINDAWI PUBLISHING CORPORATION
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
Peripheral Multiplicativity of Maps on Uniformly Closed Algebras of Continuous Functions Which Vanish at Infinity 査読
Osamu Hatori, Takeshi Miura, Hirokazu Oka, Hiroyuki Takagi
Tokyo Journal of Mathematics 32 ( 1 ) 91 - 104 2009年
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記述言語:英語 掲載種別:研究論文(学術雑誌)
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.
On surjective ring homomorphisms between semi-simple commutative Banach algebras 査読
T. Miura, S.-E. Takahasi, N. Niwa, H. Oka
Publ. Math. Debrecen 73 119 - 131 2008年12月
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Ring homomorphisms on commutative regular Banach algebras 査読
T. Miura, S.-E. Takahasi, N. Niwa
Nihonkai Math. J. 19 61 - 74 2008年1月
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A Cauchy-Euler Type Factorization of Operators 査読
Sin-Ei Takahasi, Hirokazu Oka, Takeshi Miura, Hiroyuki Takagi
Tokyo Journal of Mathematics 31 ( 2 ) 489 - 493 2008年
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記述言語:英語 掲載種別:研究論文(学術雑誌)
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.
An example of multiplicatively spectrum-preserving maps 査読
O. Hatori, T. Miura, H. Oka
Nihonkai Math. J. 18 ( 1 ) 11 - 15 2007年12月
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A perturbation of first order linear differential equation for Banach space-valued holomorphic functions 査読
T. Miura, H. Oka, S.-E. Takahasi, N. Niwa
J. Math. Inequal. 1 377 - 385 2007年9月
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2-local isometries and 2-local automorphisms on uniform algebras 査読
Osamu Hatori, Takeshi Miura, Hirokazu Oka, Hiroyuki Takagi
Hikari Ltd. 2 2491 - 2502 2007年7月
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Exponential type functional equation and its Hyers-Ulam stability 査読
Sin-Ei Takahasi, Takeshi Miura, Hiroyuki Takagi
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 329 ( 2 ) 1191 - 1203 2007年5月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:ACADEMIC PRESS INC ELSEVIER SCIENCE
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.
Prime ideals and complex ring homomorphisms on a commutative algebra 査読
Takeshi Miura, Sin-Ei Takahasi, Norio Niwa
PUBLICATIONES MATHEMATICAE-DEBRECEN 70 ( 3-4 ) 453 - 460 2007年4月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:KOSSUTH LAJOS TUDOMANYEGYETEM
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.
Unital and multiplicatively spectrum-preserving surjections between semi-simple commutative Banach algebras are linear and multiplicative 査読
Osamu Hatori, Takeshi Miura, Hiroyuki Takagi
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 326 ( 1 ) 281 - 296 2007年2月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:ACADEMIC PRESS INC ELSEVIER SCIENCE
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.
On the existence of continuous (approximate) roots of algebraic equations 査読
Kazuhiro Kawamura, Takeshi Miura
TOPOLOGY AND ITS APPLICATIONS 154 ( 2 ) 434 - 442 2007年1月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:ELSEVIER SCIENCE BV
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.
Prime ideals and complex ring homomorphisms on a commutative Banach algebra 査読
T. Miura, S.-E. Takahasi, N. Niwa
Publ. Math. Debrecen 70 453 - 460 2007年1月
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Remarks on n-th root closedness for commutative C*-algebras 査読
D. Honma, T. Miura
Nihonkai Math. J. 18 51 - 55 2007年1月
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Spectra preserving maps between commutative Banach algebras 査読
O. Hatori, T. Miura, H. Takagi
J. Math. Anal. Appl. 326 281 - 296 2007年1月
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On Wirtinger's inequality and its elementary proof 査読
Sin-Ei Takahasi, Takeshi Miura, Takahiro Hayata
Mathematical Inequalities and Applications 10 ( 2 ) 311 - 319 2007年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:Element D.O.O.
By an elementary method, we exactly determine the best possible constant and its attaining function which satisfy ∥f∥q ≤ C q∥f′∥q (1 <
q <
∝) for certain class of continuously differentiable functions on the unit interval [0.1]. © ELEMENT.
DOI: 10.7153/mia-10-27
A survey of certain algebraic equations in commutative C*-algebras 査読
Takeshi Miura, Dai Honma
Function Spaces 435 327 - 333 2007年
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記述言語:英語 掲載種別:研究論文(国際会議プロシーディングス) 出版者・発行元:AMER MATHEMATICAL SOC
Let X be a compact Hausdorff space and C(X) the commutative Banach algebra of all complex-valued continuous functions on X. We will consider the following property of C(X) introduced by Karahanjan [13]: For every f is an element of C(X) there exist g is an element of C(X) and positive integers p, q such that p does not divide q and g(p) = f(q). We will characterize the property above in terms of topology of X. We shall also compare the property to square-root closedness, or algebraic closedness of C(X).
SUPERSTABILITY OF MULTIPLIERS AND RING DERIVATIONS ON BANACH ALGEBRAS 査読
Takeshi Miura, Hirokazu Oka, Go Hirasawa, Sin-Ei Takahasi
BANACH JOURNAL OF MATHEMATICAL ANALYSIS 1 ( 1 ) 125 - 130 2007年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:BANACH MATHEMATICAL RESEARCH GROUP
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.
On a characterization of compact hausdorff space xfor which certain algebraic equations are solvable in c(x) 査読
Dai Honma, Takeshi Miura
Tokyo Journal of Mathematics 30 ( 2 ) 403 - 416 2007年
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記述言語:英語 掲載種別:研究論文(学術雑誌)
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.
A perturbation of ring derivations on Banach algebras 査読
Takeshi Miura, Go Hirasawa, Sin-Ei Takahasi
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 319 ( 2 ) 522 - 530 2006年7月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:ACADEMIC PRESS INC ELSEVIER SCIENCE
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.
On the first homology of the group of equivariant Lipschitz homeomorphisms 査読
Kojun Abe, Kazuhiko Fukui, Takeshi Miura
JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN 58 ( 1 ) 1 - 15 2006年1月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:MATH SOC JAPAN
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.
Hyers-Ulam stability of a closed operator in a Hilbert space 査読
Go Hirasawa, Takeshi Miura
Bulletin of the Korean Mathematical Society 43 ( 1 ) 107 - 117 2006年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:Korean Mathematical Society
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.
Characterizations of isometric isomorphisms between uniform algebras via nonlinear range-preserving properties 査読
O Hatori, T Miura, H Takagi
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 134 ( 10 ) 2923 - 2930 2006年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:AMER MATHEMATICAL SOC
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).
A reconsideration of Hua's inequality. Part II 査読
Hiroyuki Takagi, Takeshi Miura, Takahiro Hayata, Sin-ei Takahasi
JOURNAL OF INEQUALITIES AND APPLICATIONS 2006 ( Art. ID 21540 ) 1 - 15 2006年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:SPRINGER INTERNATIONAL PUBLISHING AG
We give a new interpretation of Hua's inequality and its generalization. From this interpretation, we know the best possibility of those inequalities.
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年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:HINDAWI PUBLISHING CORPORATION
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.
Averaging functions and inequalities due to Holder-Rogers and Minkowski 査読
S.-E. Takahasi, T. Miura, K. Sato
Sci. Math. Jpn. 62 289 - 298 2005年1月
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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 査読
Y. Miura, S.-E. Takahasi, T. Miura, M. Tsukada
J. Anal. Appl. 3 205 - 222 2005年1月
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A reconsideration of Hua's inequality 査読
Hiroyuki Takagi, Takeshi Miura, Tadashi Kanzo, Sin-Ei Takahasi
JOURNAL OF INEQUALITIES AND APPLICATIONS 2005:1 ( 1 ) 15 - 23 2005年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:HINDAWI PUBLISHING CORPORATION
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
Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras 査読
Takeshi Miura, Sin-Ei Takahasi, Go Hirasawa
JOURNAL OF INEQUALITIES AND APPLICATIONS ( 4 ) 2005年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:HINDAWI PUBLISHING CORPORATION
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
Stability of multipliers on Banach algebras 査読
Takeshi Miura, Go Hirasawa, Sin-Ei Takahasi
Int. J. Math. Math. Sci. 45 2377 - 2381 2004年10月
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A note on the Pearce-Pecaric inequalities 査読
H. Takagi, T. Miura, S.-E. Takahasi
Sci. Math. Jpn. 61 99 - 107 2004年10月
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On the best constant of Hyers-Ulam stability 査読
O. Hatori, K. Kobayashi, H. Takagi, T. Miura, S.-E. Takahasi
J. Nonlinear Convex Anal. 5 387 - 393 2004年10月
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The Hyers-Ulam stability constants of first order linear differential operators 査読
SE Takahasi, H Takagi, T Miura, S Miyajima
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 296 ( 2 ) 403 - 409 2004年8月
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:ACADEMIC PRESS INC ELSEVIER SCIENCE
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.
On convergency of a recursive sequence Xn+1 = f(Xn-1,Xn) 査読
S.-E. Takahasi, Y. Miura, T. Miura
Taiwanese J. Math. 10 631 - 638 2004年5月
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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年2月
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A note on commutative Gelfand theory for real Banach algebras 査読
S.-E. Takahasi, T. Miura, O. Hatori
J. Okayama Univ. 46 ( 1 ) 121 - 129 2004年1月
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記述言語:英語 出版者・発行元:Department of Mathematics, Faculty of Science, Okayama University
<p>Pfaffenberger and Phillips [2] consider a real and unital case of the classical commutative Gelfand theorem and obtain two representation theorems. One is to represent a unital real commutative Banach algebra A as an algebra of continuous functions on the unital homomorphism space ΦA. The other is to represent A as an algebra of continuous sections on the maximal ideal space MA. In this note, we point out that similar theorems for non-unital case hold and show that two representation theorems are essentially identical.</p>
Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations y' = λy
T. Miura, S.-M. Jung, S.-E. Takahasi
J. Korean Math. Soc. 41 ( 6 ) 995 - 1005 2004年
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On a characterization of the maximal ideal spaces of algebraically closed commutative C*-algebras 査読
Takeshi Miura, Kazuki Niijima
Proceedings of the American Mathematical Society 131 ( 9 ) 2869 - 2876 2003年9月
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記述言語:英語 掲載種別:研究論文(国際会議プロシーディングス)
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.
A characterization of Hyers-Ulam stability of first order linear differential operator. 査読
T. Miura, S. Miyajima, S.-E. Takahasi
J. Math. Anal. Appl. 286, 136--146 2003年6月
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Essential norm and stability constant for weighted composition operators on C(X). 査読
H. Takagi, T. Miura, S.-E. Takahasi
Bull. Korean Math. Soc. 40, 583--591. 2003年5月
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Ring homomorphisms on real Banach algebras 査読
Takeshi Miura, Sin-El Takahasi
International Journal of Mathematics and Mathematical Sciences 2003 ( 48 ) 3025 - 3029 2003年
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記述言語:英語 掲載種別:研究論文(学術雑誌)
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.
On the structure of the solution set of a third kind boundary value problem 査読
SE Takahasi, H Oka, T Miura
MATHEMATISCHE NACHRICHTEN 257 99 - 107 2003年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:WILEY-V C H VERLAG GMBH
We show that given any closed subset C of a real Banach space E, there is a continuous function f(t, x) which is Lipschitz continuous in its second variable such that the solution set of the corresponding third kind boundary value problem is homeomorphic to C (Theorem 1.1). In the special problem we give the infimum of Lipschitz constants L-f of such functions f (t, x) (Theorem 1.3).
Characterizations and automatic linearity for ring homomorphisms on algebras of functions. 査読
O. Hatori, T. Ishii, T. Miura, S.-E. Takahasi
Contep. Math. 328, 201--215. 2002年12月
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Hyers-Ulam stability of linear differential operator with constant cofficients. 査読
T. Miura, S. Miyajima, S.-E. Takahasi
Math. Nachr. 258, 90--96. 2002年12月
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A note on Wirtinger-Beesack's integral inequalities. 査読
S.-E. Takahasi, T. Miura
Math. Inequal. Appl. 6, 277--282. 2002年12月
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A representation of ring homomorphisms on unital regular commutative Banach algebras. 査読
T. Miura
Math, J. Okayama Univ. 44, 143--153. 2002年12月
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On the Hyers-Ulam stability of a differentiable map 査読
T.Miura
Sci. Math. Jpn., 55 2002年9月
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Polynomial identities that imply commutativity for rings 査読
H. Takagi, S.-E. Takahasi, T. Miura
Linear Algebra Appl. 341, 299-307. 2002年9月
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On the Hyers-Ulam stability of the Banach space-valued differential equation y' = λy 査読
S.-E. Takahasi, T. Miura, S. Miyajima
Bull. Korean Math. Soc., 39 2002年9月
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A note on a class of Banach algebra-valued polynomials 査読
Sin-Ei Takahasi, Osamu Hatori, Keiichi Watanabe, Takeshi Miura
International Journal of Mathematics and Mathematical Sciences 32 ( 3 ) 189 - 192 2002年
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記述言語:英語 掲載種別:研究論文(学術雑誌)
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.
A representation of ring homomorphisms on commutative Banach algebras 査読
T. Miura
Sci. Math. Jpn. 53, 515--523. 2001年9月
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On the hyers-ulam stability of real continuous function valued differentiable map 査読
Takeshi Miura, Sin Ei Takahasi, Hisashi Choda
Tokyo Journal of Mathematics 24 ( 2 ) 467 - 476 2001年
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Star ring homomorphisms between commutative Banach algebras 査読
T Miura
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 129 ( 7 ) 2005 - 2010 2001年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:AMER MATHEMATICAL SOC
We consider a (*)-ring homomorphism from a commutative Banach algebra with an involution to a commutative Banach algebra with a symmetric involution. We give the Gelfand transform of the (*)-ring homomorphism image.
On a characterization of the maximal ideal spaces of commutative C*-algebras in which every element is the square of another 査読
O Hatori, T Miura
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 128 ( 4 ) 1185 - 1189 2000年
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記述言語:英語 掲載種別:研究論文(学術雑誌) 出版者・発行元:AMER MATHEMATICAL SOC
A topological condition is given for a locally connected compact Hausdorff space on which every complex-valued continuous function is the square of another. The condition need not be necessary nor sufficient unless the space is locally connected.
On commutative C*-algebras in which every element is almost the square of another 査読
Takeshi Miura
Contemp. Math. 232 289 - 242 1999年1月
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複素関数への一歩
学術図書出版社 2010年9月
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線型代数の発想
学術図書出版社 2006年10月
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関数空間上の全射等距離写像 (集合論的・幾何学的トポロジーと種々の分野の交流)
三浦 毅
数理解析研究所講究録 1932 25 - 29 2015年1月
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記述言語:日本語 出版者・発行元:京都大学
A note on the stability of an integral equation
Takeshi Miura, Go Hirasawa, Sin-Ei Takahasi, Takahiro Hayata
Springer Optimization and Its Applications 52 207 - 222 2012年
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記述言語:英語 出版者・発行元:Springer International Publishing
Let p: ℝ→ℂ be a continuous function.We give a sufficient condition in order that the integral equation f(t) = f(0)+∫t 0 p(s) f(s)ds have the Hyers–Ulam stability. We also prove that if p has no zeros, then the sufficient condition is a necessary condition.
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年11月
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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年11月
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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年11月
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Approximate unitaries in B(H)
M. Mirzavaziri, T. Miura, M. Moslehian
East Journal of Approximations 2010年11月
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Ger-type stability of the first order linear differential equation for holomorphic functions 査読
T. Miura
Nonlinear Funct. Anal. Appl. 2010年4月
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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年12月
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記述言語:英語 出版者・発行元: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
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年12月
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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年9月
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高橋 眞映, 三浦 毅
数理解析研究所講究録 1596 38 - 41 2008年4月
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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年4月
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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年4月
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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年4月
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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年4月
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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年4月
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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年4月
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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年1月
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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年10月
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高橋 眞映, 三浦 康秀, 三浦 毅, 塚田 真
数理解析研究所講究録 1365 57 - 61 2004年4月
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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)
三浦 毅, 高橋 眞映, 平澤 剛
数理解析研究所講究録 1365 48 - 56 2004年4月
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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年1月
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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年1月
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Prime ideals and complex ring homomorphisms
三浦 毅
北海道大学数学講究録 73 2003年4月
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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年4月
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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年12月
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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年1月
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9999年04月
関数環上の実線形等距離写像の構造
関数環研究集会 2011年
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Function algebras上のisometries
つくばセミナー 2011年
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Function spaces上のisometries
つくばセミナー 2011年
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Real linear isometries between function algebras
Reaserch on preserver problems concerning to Banach algebras and its applications 2011年
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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年
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Spectrally additive surjections between uniform algebras
Sattelite Seminar in Niigata of Takahasi International 2010年
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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年
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Generalizations of spectrally multiplicative surjections between uniform algebras
The Sixth Conference on Fucntion Spaces 2010年
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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年
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Peripherally multiplicative surjections between uniform algebras
American Mathematical Society Sectional Meeting 2009年
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Standard operator algebra上のperipheral spectrum保存写像2
関数環研究集会 2009年
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Standard operator algebra上のperipheral spectrum保存写像
関数環研究集会 2008年
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A note on the stability of Volterra typw integral equation
The Twelfth International Conference of Functional Equations and Inequalities 2008年
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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年
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作用素のCauchy-Euler型因数分解
日本数学会 2007年
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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年
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Hyers-Ulam stabilityの歴史
米沢数学セミナー 2007年
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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年
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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年
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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年
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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年
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L^p空間におけるHua型方程式
日本数学会 2006年
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A generalization of Wang's inequality
日本数学会 2006年
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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年
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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年
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Banach環上のring derivationとその摂動
日本数学会 2006年
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Wirtingerの不等式とその初等的証明
日本数学会 2006年
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平均関数と不等式
日本数学会 2005年
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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年
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Hua型不等式に関する注意
日本数学会 2005年
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A Hua type inequality of L^p-spaces
実解析学シンポジウム2005 2005年
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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年
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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年
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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年
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Banach環上のmultiplierとその摂動
日本数学会 2005年
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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年
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Batler-Rassias型関数方程式とそのHyers-Ulam stability
日本数学会 2005年
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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年
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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年
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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年
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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年
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Huaの不等式再考
日本数学会 2004年
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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年
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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年
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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年
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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年
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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年
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A note on Hua-type inequalities
第13回関数空間セミナー 2004年
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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年
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A way of thinking
第13回関数空間セミナー 2004年
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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年
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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年
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On Wirtinger-Beesack type integral inequalitie
The Third International Conference on Nonlinear Analysis and Convex Analysis 2003年
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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年
詳細を見る
関数環上の荷重合成作用素のHyers-Ulam stability
日本数学会 2003年
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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年
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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年
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Huaの不等式再考
実解析学シンポジウム2003 2003年
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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年
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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年
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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年
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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年
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半可換性と不等式
第12回関数空間セミナー 2003年
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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年
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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年
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1階線形微分作用素のHyers-Ulam stability
日本数学会 2003年
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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年
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A Hua type inequality on semigroup
International Symposium of Operator Theory 2003年
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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年
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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年
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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年
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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年
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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年
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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年
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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年
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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年
詳細を見る
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年
詳細を見る
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年
詳細を見る
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年
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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年
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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年
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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年
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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年
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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年
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数学を楽しもう
第45回米沢数学セミナー 2000年
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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年
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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年
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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年
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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年
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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年
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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年
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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年
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Ring Homomorphisms from commutative Banach Algebras
International Workshop Operator Theory and Its Applications 1999年
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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年
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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年
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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年
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On Banach function algebras in which every element is square of another
The Third Conference on Function Spaces 1998年
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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年
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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年
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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年
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可換Banach環理論
1999年
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数学演習A
数学演習B
理学基礎演習
海外英語研修
海外研修
理学スタディ・スキルズ
先端科学技術総論
数理解析特別講義
微分積分学IIB
微分積分学IIA
領域概説 B (理学)
数理解析特別講義
関数空間特論
解析学序論B
解析学序論A
理学スタディ・スキルズ
複素解析学IIB
複素解析学IB
複素解析学IA
複素解析学IIA
解析学基礎1
解析学基礎2
数学基礎演習a
数学基礎演習b
専門力アクティブ・ラーニング
微分積分学III
スタディ・スキルズ(数学・情報学習法)
数理物質科学特定研究Ⅰ(数学)
数理科学文献詳読Ⅰ(数学)
数理科学研究発表演習〔中間発表〕(数学)
数理科学セミナーⅠ(数学)
Functional Analysis and its Applications
複素解析学
数学講究
複素解析特論
数学基礎A
複素解析学I
複素解析学II
スタディ・スキルズ(数学学習法)
数学英語
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