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Study on algebraic properties of maps between Banach algebras which preserve topological quantities

Research Project

Project/Area Number 19540169
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  Niigata University, 自然科学系, 教授 (70156363)

Co-Investigator(Kenkyū-buntansha) MIURA Takeshi  山形大学, 理工学研究科, 准教授 (90333989)
TAKAHASI Sin-ei  山形大学, 理工学研究科, 教授 (50007762)
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) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords関数解析 / バナッハ環 / 可換バナッハ環 / 末梢スペクトル / 等距離写像 / 等距離同形写像 / スペクトル
Research Abstract

関数環をはじめとする半単純可換バナッハ環やヒルベルト空間上の作用素からなるバナッハ環に関係した集合で乗法的にスペクトルを保存する写像や非対称に乗法的にスペクトル半径を保存する写像,またある種の距離を保存する写像の代数構造を研究し,それが線形であることや乗法的となる現象について研究を行った。このことによりバナッハ環の間の写像の保存問題についての新たな知見を得ることができた。

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (35 results)

All 2010 2009 2008 2007 Other

All Journal Article (19 results) (of which Peer Reviewed: 18 results) Presentation (16 results)

  • [Journal Article] Linear isometries of finite codimensions on Banach algebras of holomorphic functions2009

    • Author(s)
      Osamu Hatori, Kazuhiro Kasug
    • Journal Title

      Banach J. Math. Anal 3,no.2

      Pages: 109-124

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Isometries between groups of invertible elements in Banach algebras2009

    • Author(s)
      Osamu Hatori
    • Journal Title

      Studia Math 194

      Pages: 293-304

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Peripheral Multiplicativity of maps on uniformly Closed algebras of continuous functions Which vanish at infinity2009

    • Author(s)
      Osamu Hatori, Takeshi Miura, Hirokazu Oka, Hiroyuki Takagi
    • Journal Title

      Tokyo J. Math 32

      Pages: 91-104

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A Stone-Weierstrass Theorem for Banach function spaces satisfying certain separation property2009

    • Author(s)
      Eggert Briem, Osamu Hatori, Stuart J. Sidney
    • Journal Title

      J. Math. Anal. Appl 353

      Pages: 607-613

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] tability of almost multiplicative functionals2009

    • Author(s)
      Norio Niwa, Hirokazu Oka, Takeshi Miura, Sin-Ei Takahasi
    • Journal Title

      Aust. J. Math. Anal. Appl 6

      Pages: 8-8

    • Related Report
      2009 Final Research Report
  • [Journal Article] A generalization of peripherally-multiplicative surjections between standard operator algebras2009

    • Author(s)
      Takeshi Miura, Dai Honma
    • Journal Title

      Cent. Eur. J. Math 7

      Pages: 479-486

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Peripherally monomial-preserving maps between uniform algebras2009

    • Author(s)
      Osamu Hatori, Kazumi Hino, Takeshi Miura, Hirokazu Oka
    • Journal Title

      Mediteerr. J. Math 6

      Pages: 47-59

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Isometries between groups of invertible elements in Banach algebras2009

    • Author(s)
      Osamu Hatori
    • Journal Title

      Studia Math. 194

      Pages: 293-304

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Peripherally monomial-preserving maps between uniform algebras2009

    • Author(s)
      Osamu Hatori
    • Journal Title

      Mediterranean Journal of Mathematics (掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Stone-Weierstrass theorem for Banach function spaces satisfying a certain separation property2009

    • Author(s)
      Eggert Briem
    • Journal Title

      Journal of Mathematical Analysis and Applic ations (掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ring homomorphisms on Commutative regular Banach algebras2008

    • Author(s)
      Takeshi Miura, Sin-Ei Takahasi, Norio Niwa
    • Journal Title

      Nihonkai Math. J 19

      Pages: 61-74

    • NAID

      110007605515

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Ring homomorphisms on commutative regular Banach algebras2008

    • Author(s)
      Takeshi Miura
    • Journal Title

      Nihonkai Mathematica1 Journal 19

      Pages: 61-74

    • NAID

      110007605515

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An example of Multiplicatively spectrum-preserving Maps between non-isomorphic semi-simple Commutative Banach algebrs2007

    • Author(s)
      Osamu Hatori, Takeshi Miura, Hirokazu Oka
    • Journal Title

      Nihonkai Math. J 18

      Pages: 11-15

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] An example of multiplicatively spectrum-preserving maps between non-isomorphic semi-simple commutative Banach algebras2007

    • Author(s)
      Osamu Hatori
    • Journal Title

      Nihonkai Jour. Math. 18

      Pages: 11-15

    • NAID

      110006665556

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Reflections and generalization of the Mazur-Ulam theorem

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

      Rocky Mountain J. Math (掲載決定)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Generalizations of spectrally multiplicative surjections between uniform algebras

    • Author(s)
      Osamu Hatori, Takeshi Miura, Rumi Shindo, Hiroyuki Takagi
    • Journal Title

      Rendiconti. Del Circolo Mate. Palermo (掲載決定)

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Reflections and a generalization of the Mazur-Ulam theorem

    • Author(s)
      Osamu Hatori
    • Journal Title

      Rocky Mountain J.Math. (掲載決定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalizations of spectrally multiplicative surjections between uniform algebras

    • Author(s)
      Osamu Hatori
    • Journal Title

      Rendiconti del Circolo Mate. De Palermo (掲載決定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Peripheral multiplicativity of maps on uniformly closed algebras of continuous functions which vanish at infinity

    • Author(s)
      Osamu Hatori
    • Journal Title

      Tokyo Jour. Math. (掲載決定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Dunkl-Williams不等式と等号条件2010

    • Author(s)
      富永雅, 斎藤吉助
    • Organizer
      日本数学会年会
    • Place of Presentation
      慶応義塾大学矢上キャンパス
    • Year and Date
      2010-03-25
    • Related Report
      2009 Final Research Report
  • [Presentation] absolutノルムの端点のvon Neumann-Jordan定数2010

    • Author(s)
      三谷健一, 小室直人, 斎藤吉助
    • Organizer
      日本数学会年会
    • Place of Presentation
      慶応義塾大学矢上キャンパス
    • Year and Date
      2010-03-25
    • Related Report
      2009 Final Research Report
  • [Presentation] absoluteノルムの端点のJames定数2010

    • Author(s)
      三谷健一, 小室直人, 斎藤吉助
    • Organizer
      日本数学会年会
    • Place of Presentation
      慶応義塾大学矢上キャンパス
    • Year and Date
      2010-03-25
    • Related Report
      2009 Final Research Report
  • [Presentation] Isometries, symmetric Transformations on groups2010

    • Author(s)
      Osamu Hatori
    • Organizer
      International Conference on commutative Banach algebras And their applications
    • Place of Presentation
      山形大学工学部
    • Year and Date
      2010-03-21
    • Related Report
      2009 Final Research Report
  • [Presentation] Ranks of invariant subspaces of the Hardy space over the bidisk2009

    • Author(s)
      Keiji Izuchi
    • Organizer
      Joint Meeting of the KMS and the AMS
    • Place of Presentation
      梨花女子大, 韓国
    • Year and Date
      2009-12-07
    • Related Report
      2009 Final Research Report
  • [Presentation] A Mazur-Ulam theorem2009

    • Author(s)
      羽鳥理
    • Organizer
      2009年度関数環研究集会
    • Place of Presentation
      日本大学薬学部
    • Year and Date
      2009-11-26
    • Related Report
      2009 Final Research Report
  • [Presentation] 乗法的にスペクトルを保存する写像の構造定理とその拡張2009

    • Author(s)
      羽鳥理
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2009-09-24
    • Related Report
      2009 Final Research Report
  • [Presentation] A note on the stability of Volterra type integral equation2009

    • Author(s)
      Takeshi Miura
    • Organizer
      The Twelfth international Conference on Functional Equations and Inequalities
    • Place of Presentation
      Bedlewo, Poland
    • Year and Date
      2009-09-08
    • Related Report
      2009 Final Research Report
  • [Presentation] ある種のスペクトルを保存するstandard operator algebra上の写像について2009

    • Author(s)
      三浦毅
    • Organizer
      第77回米沢数学セミナー
    • Place of Presentation
      山形大学工学部
    • Year and Date
      2009-07-01
    • Related Report
      2009 Final Research Report
  • [Presentation] Peripherally multiplicInternational surjections between uniform algebras, Special Session on Banach Algebras, Topological Algebras, and Abstract Harmonic Analysis2009

    • Author(s)
      Takshi Miura
    • Organizer
      American Mathematical Society 2009 Spring Western Meeting
    • Place of Presentation
      San Francisc
    • Year and Date
      2009-04-26
    • Related Report
      2009 Final Research Report
  • [Presentation] Isometries between the Groups of invertible elements in Banach algebras, Special Session on Banach Algebras, Topological Algebras, and Abstract Harmonic Analysis2009

    • Author(s)
      Osamu Hatori
    • Organizer
      American Mathematical Society 2009 Spring Western Meeting
    • Place of Presentation
      San Francisco State University
    • Year and Date
      2009-04-26
    • Related Report
      2009 Final Research Report
  • [Presentation] Isometries between the groups of invertible elements in Banach algebras2009

    • Author(s)
      Osamu Hatori
    • Organizer
      American Math. Soc., Special Session on Banach Algebras, Topological Algebras and Abstract Harmonic Analysis
    • Place of Presentation
      San francisco State University, San Francisco, California, USA
    • Year and Date
      2009-04-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] 半単純可換Banach環の群は距離構造から復元可能である2009

    • Author(s)
      羽鳥理
    • Organizer
      つくばセミナー
    • Place of Presentation
      筑波大学
    • Year and Date
      2009-03-10
    • Related Report
      2009 Final Research Report
  • [Presentation] 乗法的にスペクトルを保存する写像の構造定理とその拡張2008

    • Author(s)
      羽鳥 理
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-24
    • Related Report
      2008 Annual Research Report
  • [Presentation] 関数環上のある種の値域保存写像2007

    • Author(s)
      羽鳥理, 三浦毅, 高木啓行
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-21
    • Related Report
      2009 Final Research Report
  • [Presentation] 関数環上のある種の値域保存写像2007

    • Author(s)
      三浦 毅
    • Organizer
      日本数学会
    • Place of Presentation
      東北大学
    • Year and Date
      2007-09-21
    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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