Updated on 2024/11/21
博士(理学) ( 2020.3 新潟大学 )
バナッハ環
等距離写像
保存問題
Natural Science / Basic analysis
Natural Science / Mathematical analysis
Niigata University Fundamental Sciences, Institute of Science and Technology, Academic Assembly Associate Professor
2024.11
Niigata University Fundamental Sciences, Graduate School of Science and Technology Associate Professor
2024.11
Niigata University Department of Science, Faculty of Science Associate Professor
2024.11
Niigata University Faculty of Science Department of Science Assistant Professor
2020.6 - 2024.10
日本数学会
Osamu Hatori, Shiho Oi
Acta Scientiarum Mathematicarum 2024.5
ISOMETRIES AND HERMITIAN OPERATORS ON SPACES OF VECTOR-VALUED LIPSCHITZ MAPS Reviewed
Shiho Oi
Journal of the Institute of Mathematics of Jussieu 1 - 18 2023.11
Isometries, Jordan *-isomorphisms and order isomorphisms on spaces of a unital $C^*$-algebra-valued continuous maps Reviewed
Shiho OI
( B93 ) 133 - 141 2023.7
Linear preservers on idempotents of Fourier algebras Reviewed
Ying-Fen Lin, Shiho Oi
Canadian Mathematical Bulletin 1 - 15 2023.5
Jordan ∗-homomorphisms on the spaces of continuous maps taking values in C∗-algebras Reviewed
Shiho Oi
Studia Math. 269 ( no.1. ) 107 - 119 2023
Tingley's problems on uniform algebras Reviewed
Osamu Hatori, Shiho Oi, Rumi Shindo Togashi
Journal of Mathematical Analysis and Applications 503 ( 2 ) 125346 - 125346 2021.11
A spherical version of the Kowalski-Slodkowski theorem and its applications Reviewed
Oi Shiho
Journal of the Australian Mathematical Society 2020
Hermitian operators and isometries on algebras of matrix-valued Lipschitz maps Reviewed
Oi Shiho
Linear and Multilinear Algebra 68 ( 6 ) 1096 - 1112 2020
Hermitian operators and isometries on injective tensor products of uniform algebras and C*-algebras Reviewed
Hatori Osamu, Kawamura Kazuhiro, Oi Shiho
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 472 ( 1 ) 827 - 841 2019.4
Algebraic reflexivity of isometry groups of algebras of Lipschitz maps Reviewed
Oi Shiho
LINEAR ALGEBRA AND ITS APPLICATIONS 566 167 - 182 2019.4
2-local isometries on function spaces Reviewed
O.Hatori, S.Oi
Contemporary Mathematics 737 89 - 106 2019
Isometries on Banach algebras of vector-valued maps Reviewed
Hatori Osamu, Oi Shiho
ACTA SCIENTIARUM MATHEMATICARUM 84 ( 1-2 ) 151 - 183 2018
Peculiar homomorphisms between algebras of vector-valued maps Reviewed
Hatori Osamu, Oi Shiho, Takagi Hiroyuki
STUDIA MATHEMATICA 242 ( 2 ) 141 - 163 2018
Hermitian operators on Banach algebras of vector-valued Lipschitz maps (vol 452, pg 378, 2017) Reviewed
Hatori Osamu, Oi Shiho
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 453 ( 2 ) 1151 - 1152 2017.9
Hermitian operators on Banach algebras of vector-valued Lipschitz maps Reviewed
Hatori Osamu, Oi Shiho
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 452 ( 1 ) 378 - 387 2017.8
Peculiar homomorphisms on algebras of vector-valued continuously differentiable maps Reviewed
O.Hatori, S.Oi, H.Takagi
Linear and Nonlinear Analysis 3 101 - 109 2017
Homomorphisms between algebras of Lipschitz functions with the values in function algebras Reviewed
Oi Shiho
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 444 ( 1 ) 210 - 229 2016.12
OI SHIHO, HATORI OSAMU
数理解析研究所講究録 ( 2035 ) 168 - 172 2017.7
Unital surjective linear isometries on Lipchitz algebras taking values in primitive $C^{*}$-algebras
Shiho OI
Workshop on Function spaces and related topics 2023.4
Surjective isometries and Hermitian operators on vector-valued Lipschitz algebras Invited
Shiho Oi
2022 Japan-China International Conference on matrix theory with applications 2022.12
C∗ 環に値をとるリプシッツ関数のなすバナッハ環上の等距離写像 Invited
大井志穂
第11 回信州関数解析シンポジウム 2022.11
C∗ 環値リプシッツ環の間の Jordan* 同型写像とその応用
大井志穂
2022 年度 関数環研究集会 2022.11
Kowalski-S\l odkowskiの定理と2-local等距離写像 Invited
大井志穂
第 6 回幾何学的群論ワークショップ 2022.10
2-local isometries on commutative Banach algebras Invited
Shiho Oi
Women in Operator Theory 2022.10
C*環に値をとるリプシッツ環上のJordan* 準同型写像
大井志穂
日本数学会 2022年度秋季総合分科会 2022.9
C*環に値をとる連続写像のなすバナッハ環上の保存問題 Invited
大井志穂
第69回トポロジ―シンポジウム 2022.8
Jordan *-homomorphisms on *-algebras of vector-valued continuous maps Invited
Shiho Oi
Operators on Banach algebras and related topics, Tarbiat Modares University, Iran 2022.7
Surjective linear isometries on Banach algebras of continuous functions Invited
Shiho Oi
Trojan Math Seminar, Troy University 2024.1
Isometries between groups of invertible elements in Fourier-Stieltjes algebras Invited
Shiho Oi
Joint Mathematics Meetings 2024 (AMS Special Session on New Faces in Operator Theory and Function Theory) 2024.1
フーリエ環のべき等元を保存する写像
大井志穂
2023年度 関数環研究集会 2023.12
Linear preservers on idempotents of Fourier algebras
Shiho OI
Recent Progress in Operator Theory and its Applications (RIMS 共同研究) 2023.11
バナッハ環におけるノルム構造，代数構造，順序構造の関係 Invited
大井志穂
日本数学会 秋季総合分科会 2023 2023.9
Linear operators on Fourier algebras preserving idempotents
Shiho OI
The 6th Niigata Seminar 2023.8
バナッハ環上の全射線形等距離写像について
大井志穂
東京都立大学・幾何学セミナー 2023.6
行列値リプシッツ環上の 全射線形等距離写像の代数的反射性
大井志穂
2023年 日本数学会年会 2023.3
C*環に値をとる連続写像のなすバナッハ環上の 等距離写像
大井志穂
第8 回山陰基礎論と数学およびその周辺の研究集会 2023.1
C*環に値をとる連続写像のなすバナッハ環上のJordan* 同型写像
大井志穂
2021年度関数環研究集会 2021.12
リプシッツ写像のなすBanach 環の距離構造と代数構造 Invited
2021年度ジェネラルトポロジーシンポジウム 2021.12
Surjective linear isometries on unital C*-algebra valued Lipschitz algebras Invited
Shiho Oi
Research on preserver problems on Banach algebras and related topics, 京都大学(数理解析研究所) 2021.10
C*環に値をとるリプシッツ環の間の等距離写像 Invited
大井志穂
第60 回実函数論・函数解析学合同シンポジウム 2021.9
Surjective isometries on Banach algebras of Lipschitz maps taking values in a unital C*-algebra Invited
Shiho Oi
the 8th European Congress of Mathematics-8ECM, Minisymposum: Recent Developments on Preservers 2021.7
2-local isometries on commutative Banach algebras
2021.3
Order isomorphisms on spaces of continuous maps
2020.11
行列環に値をとるLipschitz環の間の全射等距離写像について
大井志穂
日本数学会2020年度秋季総合分科会 2020.9
Reflexivity of isometry groups Invited
大井志穂
RIMS共同研究（公開型）「様々な関数空間上の等距離写像の研究」 2020.1
2-local isometries on spaces of continuous functions Invited
大井志穂
作用素論・作用素環論研究集会 2019.12
Hermitian operators on Banach algebras of vector-valued continuous maps
Oi Shiho
関数環研究集会 2019.12
関数空間の間の2-local map について Invited
大井志穂
第61 回関東作用素論セミナー 2019.7
Hermitian operators and surjective isometries on vector-valued Lipschitz spaces Invited International conference
Oi Shiho
Women in Operator Theory and its Applications 2019.6
2-local maps on spaces of continuous functions
羽鳥理, 大井志穂
日本数学会2019 年度年会 2019.3
Algebraic reflexivity of the group of surjective linear isometries International conference
Oi Shiho
関数環研究集会 2018.12
Hermitian operators on spaces of vector-valued Lipschitz maps Invited International conference
Oi Shiho
Researches on theory of isometries and preserver problems from a various point of view(RIMS Conference) 2018.2
Surjective linear isometries on vector-valued Lipschitz algebras Invited International conference
Oi Shiho
The international meeting on Commutative algebra, Banach algebras (preserver probrem), Hypergroups and their related topics 2016.11
Peculiar isomorphisms on algebras of Lipschitz maps with values in uniform algebras Invited International conference
Oi Shiho, Hatori Osamu, Takagi HIroyuki
The international meeting on Commutative algebra, Banach algebras (preserver probrem), Hypergroups and their related topics 2016.11
Peculiar homomorphisms on commutative Banach algebras of vector-valued functions Invited International conference
Oi Shiho, Hatori Osamu, Takagi HIroyuki
Researches on isometries from various view points (RIMS Workshop) 2016.11
Hermitian operators on Banach algebras of vector-valued Lipschitz maps Invited International conference
Oi Shiho
Researches on isometries from various view points (RIMS Workshop) 2016.11
Homomorphisms on vector-valued Banach function algebras
Oi Shiho, Hatori Osamu, Takagi HIroyuki
第90 回米沢数学セミナー 2016.7
On isometries of vector-valued Lipschitz algebras
Hatori Osamu, Oi Shiho
第90 回米沢数学セミナー 2016.7
Lipschitz 環の写像に対する代数的反射性
大井志穂
つくばセミナー 2016.3
Lipschitz 環上の準同形写像について Invited
大井志穂
第89 回米沢数学セミナー「学術講演会」 2016.2
関数環に値をとるLipschitz 環上の準同形写像について
大井志穂
関数環研究集会 2015.12
Peripheral spectrum conditions for triple products of Lipschitz functions on non-compact metric spaces Invited International conference
Oi Shiho
International Conference on Preserver Problems and Related Topics 2015.5
Isometries on Banach algebras
Grant number：21K13804
2021.4 - 2025.3
System name：Grants-in-Aid for Scientific Research
Research category：Grant-in-Aid for Early-Career Scientists
Awarding organization：Japan Society for the Promotion of Science
Authorship：Principal investigator Grant type：Competitive
Grant amount：\4420000 （ Direct Cost: \3400000 、 Indirect Cost：\1020000 ）
Banach空間上のスペクトル保存写像とその応用
Grant number：20K03650
2020.4 - 2024.3
System name：科学研究費助成事業
Research category：基盤研究(C)
Awarding organization：日本学術振興会
三浦 毅, 大井 志穂
Grant amount：\4290000 （ Direct Cost: \3300000 、 Indirect Cost：\990000 ）
今年度は主に，局所的な等距離写像（local isometries)に関する研究を行い，いくつかの結果を得た．まず単位閉区間[0,1]上で定義された連続微分可能な複素関数の全体C^1([0,1])に対して，その間の2-local real linear isometryを考察した．一般にTがBanach空間Bの間の2-local isometryであるとは，Bの任意の2点f, gに対して，S(f)=T(f)かつS(g)=T(g)をみたすB上の全射複素線形等距離写像Sが存在することである．この概念は，P.Semrlが導入したlocal mapのアイディアをもとに，Molnarによって提示され，その後2-local isometryの研究は活発になされるようになった．C^1([0,1])には様々なノルムが与えられることが知られる中で，我々は特に|f(0)|+||f'||をノルムとするBanach空間C^1([0,1])に対する2-local real linear isometryを解明した．ここで||g||はgの最大絶対値ノルムである．また，複素平面の単位開円板D上の正則関数で，その導関数がp乗可積分であるもの全体S^p(D)に対して，近似的局所的等距離写像(approximate local isometry)の概念を導入し，その構造を研究した．ここでS^p(D)の間の写像Tがapproximate local isometryであるとは，S^p(D)の任意の2点f, gに対してS^p(D)上の全射複素線形等距離写像の列{U_n}が存在して，n→∞のときノルムの意味でU_n(f)はT(f)に，U_n(g)はT(g)に収束することである．このとき，S^p(D)上の任意のapproximate local isometryは全射等距離写像であることを示すとともに，approximate 2-lolcal isometryの概念も自然な形で導入し，S^p(D)上のapproximate 2-local isometryは全射複素線形等距離写像であることを示した．
Advanced Theory of Function Spaces
The world of Mathematics
Basic Practice on Mathematics a
Seminar in Mathematics
Fundamentals of Analysis 2
Fundamentals of Analysis 1
Basic Practice on Mathematics b
Mathematics Exercise B
Set and Mapping
Mathematics Exercise A
自然科学総論I
領域概説 B (理学)
日本事情自然系A
先端科学技術総論
数理解析特別講義
理学基礎演習
数学基礎演習b
数学講究
解析学基礎1
数学基礎演習a
関数空間特論
解析学基礎2
関数空間論
数学の世界
理学スタディ・スキルズ
専門力アクティブ・ラーニング
数学演習A
数学演習B
集合と写像
