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Studies on structures and isometries of commutative Banach algebras

Research Project

Project/Area Number 23540193
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionShinshu University

Principal Investigator

TAKAGI Hiroyuki  信州大学, 学術研究院理学系, 教授 (20206725)

Co-Investigator(Kenkyū-buntansha) HATORI Osamu  新潟大学, 自然科学系, 教授 (70156363)
Co-Investigator(Renkei-kenkyūsha) MIURA Takeshi  新潟大学, 自然科学系, 教授 (90333989)
UEKI Sei-Ichiro  茨城大学, 工学部, 准教授 (70512408)
Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords関数解析学 / バナッハ環 / 保存問題 / 合成作用素
Outline of Final Research Achievements

Inspired by the preserver problem of Banach algebras, we consider the characterization of (not necessarily linear) isometries between continuous function spaces. Here a continuous function space means a linear space consisting of (not necessarily all) continuous functions with the supremum norm. We prove that if continuous function spaces A and B satisfy a certain separation property, then every isometry from A onto B is represented by using a weighted composition operator and its complex conjugate on the Choquet boundary of B.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report

Research Products

(19 results)

All 2015 2014 2013 2012 2011 Other

All Journal Article Presentation

  • [Journal Article] Ulam type stability problems for alternative homomorphisms2014

    • Author(s)
      S-E. Takahasi, M. Tsukada, T. Miura, H. Takagi and K. Tanahashi
    • Journal Title

      Journal of Inequalities and Applications

      Volume: 2014 Pages: 1-13

    • DOI

      10.1186/1029-242x-2014-228

    • NAID

      120006650875

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Isometies of the unitary groups in C^*-algebras2014

    • Author(s)
      O. Hatori
    • Journal Title

      Studia Math.

      Volume: 221 Pages: 61-86

    • DOI

      10.4064/sm221-1-4

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Real-linear isometries between subspaces of continuous functions2014

    • Author(s)
      H. Koshimizu, T. Miura, H. Takagi and S.-E. Takahasi
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 413 Pages: 229-241

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in C^*-algebras2014

    • Author(s)
      O. Hatori and L Molnar
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 409 Pages: 158-167

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Isometries between groups of invertible elements in C*-algebras2012

    • Author(s)
      O. Hatori and K. Watanabe
    • Journal Title

      Studia Math.

      Volume: 209 Pages: 103-106

    • Related Report
      2012 Research-status Report
  • [Journal Article] Isometries of the unitary groups2012

    • Author(s)
      O. Hatori and L. Molnar
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 140 Pages: 2141-2154

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

    • Author(s)
      H. Takagi, H. Koshimizu and H. Ariizumi
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 377 Pages: 135-144

    • NAID

      120004966386

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Spectral radii conditions for isomorphisms between unital semisimple commutative Banach algebras2011

    • Author(s)
      G. Hirasawa, T. Miura and H. Takagi
    • Journal Title

      Contemp. Math.

      Volume: 547 Pages: 125-134

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

    • Author(s)
      O. Hatori
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 376 Pages: 74-83

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] 直積空間上のシフト作用素2015

    • Author(s)
      高木啓行, 古清水大直
    • Organizer
      第2回山陰基礎論・解析学研究集会
    • Place of Presentation
      鳥取県米子市国際ファミリープラザ
    • Year and Date
      2015-01-24 – 2015-01-25
    • Related Report
      2014 Annual Research Report
  • [Presentation] SO(4)上のある写像について2014

    • Author(s)
      羽鳥理
    • Organizer
      関数環研究集会
    • Place of Presentation
      早稲田大学教育学部
    • Year and Date
      2014-09-18 – 2014-09-19
    • Related Report
      2014 Annual Research Report
  • [Presentation] 直積空間と等長作用素2013

    • Author(s)
      高木啓行・古清水大直
    • Organizer
      つくばセミナー
    • Place of Presentation
      筑波大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Isometries on the unitary groups2012

    • Author(s)
      O. Hatori
    • Organizer
      Conference on Mathematics and Statistics
    • Place of Presentation
      University of Memphis
    • Related Report
      2012 Research-status 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
      筑波大・自然科学系
    • Related Report
      2011 Research-status Report
  • [Presentation] Real-linear isometries between subspaces of continuous functions2011

    • Author(s)
      H. Koshimizu, T. Miura, H. Takagi and S.-E. Takahasi
    • Organizer
      Research on preserver problems concerning to Banach algebras and its applications
    • Place of Presentation
      京大・数理研
    • Related Report
      2011 Research-status Report
  • [Presentation] Criteria for the equivalence of LCA groups2011

    • Author(s)
      O. Hatori
    • Organizer
      Workshop on commutative Banach algebra 2011
    • Place of Presentation
      奈良教育大
    • Related Report
      2011 Research-status Report
  • [Presentation] Ulam type stability problems for alternative homomorphisms2011

    • Author(s)
      S.-E. Takahasi, T. Miura, H. Takagi and K. Tanahashi
    • Organizer
      第20回関数空間セミナー
    • Place of Presentation
      北大・理
    • Related Report
      2011 Research-status Report
  • [Presentation] 保存問題における関数空間上の等距離写像について

    • Author(s)
      高木啓行、古清水大直
    • Organizer
      山陰基礎論・解析学セミナー
    • Place of Presentation
      米子高専
    • Related Report
      2013 Research-status Report
  • [Presentation] exp A 上の preserver problem について

    • Author(s)
      羽鳥理
    • Organizer
      関数環研究集会
    • Place of Presentation
      クロスパルにいがた
    • Related Report
      2013 Research-status Report

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Published: 2011-08-04   Modified: 2019-07-29  

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