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Study on preserver problems on Banach alebras

Research Project

Project/Area Number 22540178
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionNiigata University

Principal Investigator

HATORI Osamu  新潟大学, 自然科学系, 教授 (70156363)

Co-Investigator(Kenkyū-buntansha) MIURA Takeshi  山形大学, 理工学研究科, 教授 (90333989)
TAKAGI Hiroyuki  信州大学, 理学部, 教授 (20206725)
IZUCHI Keiji  新潟大学, 自然科学系, 教授 (80120963)
SAITO Kichisuke  新潟大学, 自然科学系, 教授 (30018949)
WATANABE Keiichi  新潟大学, 自然科学系, 准教授 (50210894)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywordsバナッハ環 / C*環 / 等距離写像 / 代数構造 / ユニタリー群 / 正値可逆元 / Thmpson距離
Research Abstract

We give a structure theorem for isometries between the general linear groups of Banach algebras. As an application of it, we deduce the form of isometries between the general linear group of C*-algebras. We get a non-commutative Mazur-Ulam theorem and we describe the form of isometries between the full unitary group of a Hilbert space. We also get a result on the maps between certain commutative Banach algebras which preserve the norm non-symmetrically. We describe the form of the multiplicative isometries between F-algebras of holomorphic functions.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (65 results)

All 2013 2012 2011 2010 Other

All Journal Article (41 results) (of which Peer Reviewed: 41 results) Presentation (24 results) (of which Invited: 4 results)

  • [Journal Article] Another consequence of Tanahashi's argument on best possibility of the grand Furuta inequality2013

    • Author(s)
      Tatsuya Koizumi and Keiichi Watanabe
    • Journal Title

      Cent. Eur. J. Math

      Volume: vol.11 Pages: 368-375

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Reflections and a generalization of the Mazur-Ulam theorem2012

    • Author(s)
      Osamu Hatori, Kiyotaka Kobayashi,Takeshi Miura, Sin-Ei Takahasi
    • Journal Title

      Rocky Mountain J. Math

      Volume: vol.42 Pages: 117-150

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stevo Stevicand Sei-Ichiro Ueki, Multiplicative isometries on F-algebras of holomorphic functions2012

    • Author(s)
      Osamu Hatori, Yasuo Iida
    • Journal Title

      Abstr. Appl. Anal

      Pages: 16-16

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Isometries of the unitary group2012

    • Author(s)
      Osamu Hatori and Lajos Molnar
    • Journal Title

      Proc. Amer. Math. Soc

      Volume: vol.140 Pages: 2127-2140

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] New criteria for equivalence of locally compact abelian groups2012

    • Author(s)
      Osamu Hatori
    • Journal Title

      J. Group Theory

      Volume: vol.15 Pages: 271-277

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Isometries between groups of invertible elements in C*-algebras2012

    • Author(s)
      Osamu Hatori and Keiichi Watanabe
    • Journal Title

      Studia Math

      Volume: vol.209 Pages: 103-106

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A remark on extension of order preserving operator inequality2012

    • Author(s)
      Tatsuya Koizumi and Keiichi Watanabe
    • Journal Title

      J. Math. Inequal

      Volume: vol.6 Pages: 119-124

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Isometries and maps compatible with inverted Jordan triple products2012

    • Author(s)
      Osamu Hatori, Go Hirasawa, TakeshiMiura and Lajos Molnar
    • Journal Title

      Tokyo J. Math

      Volume: vol.35 Pages: 385-410

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability of the Banach space valued Chebyshev differential equation2012

    • Author(s)
      Takeshi Miura, Sin-Ei Takahasi, Takahiro Hayata and Kotaro Tanahashi
    • Journal Title

      Appl. Math. Lett

      Volume: vol.25 Pages: 1976-1979

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note on the stability of an integral equation2012

    • Author(s)
      Takeshi Miura, Go Hirasawa and Takahiro Hayata
    • Journal Title

      Funct. Equ. Math. Anal

      Volume: vol.52 Pages: 207-222

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On a simple range of parameters of the grand Furuta inequality2012

    • Author(s)
      Keiichi Watanabe
    • Journal Title

      Int. Math. Forum

      Volume: vol.7 Pages: 2897-2902

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Dunkl-Williams constant of symmetric octagonal norms on R^22012

    • Author(s)
      Hiroyoshi Mizuguchi and Kichi-Suke Saito
    • Journal Title

      Nihonkai Math. J

      Volume: vol.23 Pages: 93-113

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dieu Quang and Shuichi Ohno, Composition operators induced by analytic maps to the polydisk2012

    • Author(s)
      Kei Ji Izuchi
    • Journal Title

      Canad. J. Math

      Volume: vol.64 Pages: 1329-1340

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Isometries and maps compatible with inverted Jordan triple products2012

    • Author(s)
      Osamu Hatori
    • Journal Title

      Tokyo J. Math.

      Volume: 35

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stability of the Banach space valued Chebyshev differential equation2012

    • Author(s)
      Takeshi Miura
    • Journal Title

      Appl. Math. Lett.

      Volume: 25

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on the stability of an integral equation2012

    • Author(s)
      Takeshi Miura
    • Journal Title

      Functional Equations in Mathematical Analysis, Springer Optimization and Its Applications

      Volume: 52

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On a simple range of parameters of the grand Furuta inequality2012

    • Author(s)
      K. Watanabe
    • Journal Title

      International Mathematical Forum

      Volume: 7

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Dunkl-Williams constant of symetric octagonal norms on $\Bbb R^2$2012

    • Author(s)
      Hiroyoshi Mizuguchi
    • Journal Title

      Nihonkai Math. J.

      Volume: 23

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Composition operators induced by analytic maps to the polydisk2012

    • Author(s)
      Kei Ji Izuchi
    • Journal Title

      Canad. J. Math.

      Volume: 64

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Reflections and a generalization of the Mazur-Ulam theorem2012

    • Author(s)
      Osamu Hatori
    • Journal Title

      Rocky Mountain J.Math.

      Volume: 42 Pages: 117-150

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multiplicative isometries on F-algebras of holomorphic functions2012

    • Author(s)
      羽鳥理
    • Journal Title

      Abstract and Applied Analysis

      Volume: 2012 Issue: 1 Pages: 1-16

    • DOI

      10.1155/2012/125987

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Isometries of the unitary groups2012

    • Author(s)
      Osamu Hatori
    • Journal Title

      Proc.Amer.Math.Soc.

      Volume: 140 Pages: 2141-2154

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] New criteria for equivalence of locally compact abelian groups2012

    • Author(s)
      Osamu Hatori
    • Journal Title

      Jour.Group Theory

      Volume: 15 Pages: 271-277

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Algebraic properties ofisometries between groups of invertible elements in Banach algebras2011

    • Author(s)
      Osamu Hatori
    • Journal Title

      J. Math. Anal. Appl

      Volume: vol.376 Pages: 84-93

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Thomas Tonev and Rebekah Yates, Spectral preservers in commutative Banach algebras2011

    • Author(s)
      Osamu Hatori, Scott Lambert, AaronLuttman, Takeshi Miura
    • Journal Title

      Contemp. Math

      Volume: vol.547 Pages: 103-123

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Backward shifts on function algebras2011

    • Author(s)
      Hiroyuki Takagi, Hironao Koshimizu andHiroaki Ariizumi
    • Journal Title

      J. Math. Anal. Appl

      Volume: vol.377 Pages: 135-144

    • NAID

      120007114269

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Multiplicative isometries on the Smirnov class2011

    • Author(s)
      Osamu Hatori and Yasuo Iida
    • Journal Title

      Cent. Eur. J. Math

      Volume: vol.9 Pages: 1051-1056

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On best possibility of an extension of Furuta inequality2011

    • Author(s)
      Tatsuya Koizumi and Keiichi Watanabe
    • Journal Title

      Int. J. Funct. Anal. Oper. Theorey Appl

      Volume: vol.3 Pages: 155-161

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Ranks of invariant subspaces of the Hardy space over the bidisk2011

    • Author(s)
      Kei Ji Izuchi, Kou Hei Izuchi and Yuko Izuchi
    • Journal Title

      J. Reine Angew. Math

      Volume: vol.659 Pages: 101-139

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Some geometrical constants of absolute normalized norms on $¥Bbb R^2$2011

    • Author(s)
      Hiroyasu Mizuguchi and Kichi-Suke Saito
    • Journal Title

      Ann. Funct. Anal

      Volume: vol.2 Pages: 22-33

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Algebraic properties of isometries between groups of invertibleelements in Banach algebras2011

    • Author(s)
      Osamu Hatori
    • Journal Title

      Jour.Math.Anal.Appl.

      Volume: 376 Pages: 74-83

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Backward shifts on function algebras2011

    • Author(s)
      Hiroyuki Takagi
    • Journal Title

      Jour.Math.Anal.Appl.

      Volume: 377 Pages: 135-144

    • NAID

      120007114269

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spectral preservers in commutative Banach algebras2011

    • Author(s)
      Osamu Hatori
    • Journal Title

      Contemp.Math.

      Volume: 547 Pages: 103-123

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Multiplicative isometries on the Smirnov class2011

    • Author(s)
      Osamu Hatori
    • Journal Title

      Cent.Eur.J.Math.

      Volume: 9 Pages: 1051-1056

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On best possibility of an extension of Furuta inequality2011

    • Author(s)
      T.Koizumi
    • Journal Title

      Int.J.Funct.Anal.Oper.Theory Appl.

      Volume: 3 Pages: 155-161

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ranks of invariant subspaces of the Hardy space over the bidisk2011

    • Author(s)
      Kei Ji Izuchi
    • Journal Title

      J.Reine Angew.Math.

      Volume: 659 Pages: 101-139

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some geometrical constants of absolute normalized norms on R^22011

    • Author(s)
      Hiroyasu Mizuguchi
    • Journal Title

      Ann.Funct.Anal.

      Volume: 2 Pages: 22-33

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras2010

    • Author(s)
      Osamu Hatori, Go Hirasawa, and TakeshiMiura
    • Journal Title

      Cent. Eur. J. Math

      Volume: vol.8 Pages: 597-601

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Additively spectral-radius preserving surjections between unital semisimple commutative Banach algebras2010

    • Author(s)
      Osamu Hatori
    • Journal Title

      Cent.Eur.J.Math.

      Volume: 8 Pages: 597-601

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Algebraic properties.of isometries between groups of invertible elements in Banach algebras

    • Author(s)
      Osamu Hatori
    • Journal Title

      J.Math.Anal.Appl.

      Volume: (掲載予定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spectral preservers in commutative Banach algebras

    • Author(s)
      Osamu Hatori
    • Journal Title

      Contemp.Math.

      Volume: (掲載予定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Unitary群の構造と等距離写像2013

    • Author(s)
      羽鳥 理
    • Organizer
      つくばセミナー
    • Place of Presentation
      筑波大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] 関数空間上の全射等距離写像と端点の性質2013

    • Author(s)
      三浦 毅
    • Organizer
      つくばセミナー
    • Place of Presentation
      筑波大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Isometries on theunitary groups2012

    • Author(s)
      Osamu Hatori
    • Organizer
      International Conferenceon Mathematics and Statics
    • Place of Presentation
      Univ. Memphis, USA
    • Year and Date
      2012-05-16
    • Related Report
      2012 Final Research Report
  • [Presentation] Surjective isometreisbetween function algebras2012

    • Author(s)
      Takashi Miura
    • Organizer
      International Conference on Mathematics and Statics
    • Place of Presentation
      Univ. Memphis, USA
    • Year and Date
      2012-05-15
    • Related Report
      2012 Final Research Report
  • [Presentation] Surjective isometriesbetween function spaces2012

    • Author(s)
      Takashi Miura
    • Organizer
      Colloqium Series
    • Place of Presentation
      University of Montana, USA
    • Year and Date
      2012-05-11
    • Related Report
      2012 Final Research Report
  • [Presentation] Isometries on groups andits applications2012

    • Author(s)
      Osamu Hatori
    • Organizer
      Department of Mathematical Sciences, Colloqium Series
    • Place of Presentation
      University of Montana, USA
    • Year and Date
      2012-05-10
    • Related Report
      2012 Final Research Report
  • [Presentation] ユニタリー群上の等距離写像2012

    • Author(s)
      羽鳥理
    • Organizer
      つくばセミナー
    • Place of Presentation
      つくば大学
    • Year and Date
      2012-03-05
    • Related Report
      2011 Annual Research Report
  • [Presentation] 特殊直交群上の等距離写像(1)2012

    • Author(s)
      阿部 敏一
    • Organizer
      2012年度関数環研究集会
    • Place of Presentation
      日本大学理工学部
    • Related Report
      2012 Annual Research Report
  • [Presentation] 特殊直交群上の等距離写像(2)2012

    • Author(s)
      阿部 敏一
    • Organizer
      2012年度関数環研究集会
    • Place of Presentation
      日本大学理工学部
    • Related Report
      2012 Annual Research Report
  • [Presentation] Isometries on the unitary groups2012

    • Author(s)
      Osamu Hatori
    • Organizer
      International Conference on Mathematics and Statistics
    • Place of Presentation
      University of Memphis
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Isometries on groups and its applications2012

    • Author(s)
      Osamu Hatori
    • Organizer
      University of Montana
    • Place of Presentation
      University of Montana
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Surjective Isometries between function algebras2012

    • Author(s)
      Takeshi Miura
    • Organizer
      International Conference on Mathematics and Statictics
    • Place of Presentation
      University of Memphis
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Surjective Isometries between function spaces2012

    • Author(s)
      Takeshi Miura
    • Organizer
      Department of Mathematical Sciences, Colloquium Series
    • Place of Presentation
      University of Montana
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Ulam type stability problems for alternative homomorphisms2011

    • Author(s)
      S.-E.Takahasi
    • Organizer
      第20回関数空間セミナー
    • Place of Presentation
      北海道大学理学部
    • Year and Date
      2011-12-24
    • Related Report
      2011 Annual Research Report
  • [Presentation] Criteria for the equivalence of LCA groups2011

    • Author(s)
      Osamu Hatori
    • Organizer
      Workshop on Commutative Algebra 2011 in Nara University of Education-Commutative Algebra and related topics--
    • Place of Presentation
      奈良教育大学
    • Year and Date
      2011-11-04
    • Related Report
      2011 Annual Research Report
  • [Presentation] On recent results of order preserving operator inequalities2011

    • Author(s)
      Keiichi Watanabe
    • Organizer
      Banach環に関わるpreserver problemの研究とその応用
    • Place of Presentation
      東都大学数理解析研究所
    • Year and Date
      2011-11-02
    • Related Report
      2011 Annual Research Report
  • [Presentation] Real-linear isometries between subspaces of continuous functions2011

    • Author(s)
      K.Koshimizu
    • Organizer
      Banach環に関わるpreserver problemの研究とその応用
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-11-01
    • Related Report
      2011 Annual Research Report
  • [Presentation] Gleason部分に関するH∞の閉イデアルの構造2011

    • Author(s)
      泉池敬司
    • Organizer
      第50回実函数論・函数解析学合同シンポジュウム
    • Place of Presentation
      東京女子大学
    • Year and Date
      2011-08-09
    • Related Report
      2012 Final Research Report
  • [Presentation] Gleason部分に関するH∞の閉イデアルの構造2011

    • Author(s)
      泉池敬司
    • Organizer
      第50回実函数論・函数解析学合同シンポジュウム
    • Place of Presentation
      東京女子大学(招待講演)
    • Year and Date
      2011-08-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] How to calculate thegeometrical constants of Banach spaces2011

    • Author(s)
      Kichi-Suke Saito
    • Organizer
      The seventh Internationa Conference on Nonlinear Analysis and Convex Analysis
    • Place of Presentation
      Pukyong National University, Busan Korea
    • Year and Date
      2011-08-03
    • Related Report
      2012 Final Research Report
  • [Presentation] How to calculate the geometrical constants of Banach spaces2011

    • Author(s)
      Kichi-Suke Saito
    • Organizer
      The seventh International Conference on Nonlinear Analysis and Convex Anal-Ysis
    • Place of Presentation
      Pukyong National University, Busan Korea(招待講演)
    • Year and Date
      2011-08-03
    • Related Report
      2011 Annual Research Report
  • [Presentation] Algebraic structures ofisometries on groups2010

    • Author(s)
      Osamu Hatori
    • Organizer
      The sixth Conference on Function Spaces
    • Place of Presentation
      Southern Illinois University at Edwardsville, USA
    • Year and Date
      2010-05-19
    • Related Report
      2012 Final Research Report
  • [Presentation] Algebraic structures of isometries on groups2010

    • Author(s)
      Osamu Hatori
    • Organizer
      Conference on Function Spaces
    • Place of Presentation
      Southern Illinois Univ;USA.
    • Year and Date
      2010-05-19
    • Related Report
      2010 Annual Research Report
  • [Presentation] Generalizations ofspectrally multiplicative surjections between uniform algebras2010

    • Author(s)
      Takashi Miura
    • Organizer
      The sixth Conference on Function Spaces
    • Place of Presentation
      Southern Illinois University at Edwardsville, USA
    • Year and Date
      2010-05-18
    • Related Report
      2012 Final Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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