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2007 Fiscal Year Annual Research Report

可換Banach環及びBanachmodulesの分類とその応用

Research Project

Project/Area Number 19540159
Research InstitutionYamagata University

Principal Investigator

高橋 眞映  Yamagata University, 大学院・理工学研究科, 教授 (50007762)

Co-Investigator(Kenkyū-buntansha) 羽鳥 理  新潟大学, 自然科学系, 教授 (70156363)
Keywordscommutative Banach algebra / Segel algebra / Gelfand transform / quasi-topology / local multiplier / approximate identity / Hyers-Ulam stability / Hlawka's inequality
Research Abstract

本研究はGelfand変換像及びHelgason-Wang変換像を特徴付けることにより、可換Banach環の分類を行い、その本質を探ることが主目的であった。実際これらの特徴付け問題から自然にBSE環とBED環という可換Banach環のクラスが生まれ、従って我々は可換Banach環を4つのクラス:(1)BSE and BED,(II)BSE and not BED,(III)BED and not BSE,(IV)not BED and not BSEに分類することが出来た。そこでそれぞれに属する環の具体例を考察した結果、どのクラスについてもある程度豊富にあることが分かり、これを纏めたものがドイツの数学雑誌Math. Nachr.,280,No.1-2(2007),105-126に掲載された。また可換Banach環のdense idealとして定義される抽象p Segal環を導入し、local multiplierと呼ばれるGelfand空間上の複素数値連続関数が自然に導出する抽象Segal環のBSE性とBED性を調査した。これらの結果は前出の数学雑誌に投稿中である。また可換Banach環の分類に関連して、指数型汎関数方程式、Banach空間値線型微分方程式、Hilbert空間上の正規作用素などのHyers-Ulam stabilityに関する結果や一般Hlawka不等式、Banach空間上の三角不等式に関する結果などを得た。
これらの結果はしかるべきジャーナルに掲載または掲載予定である。詳細は研究発表の欄を参照されたい。

  • Research Products

    (14 results)

All 2008 2007 Other

All Journal Article (12 results) (of which Peer Reviewed: 12 results) Presentation (2 results)

  • [Journal Article] Prime ideals and complex ring homomorphisms on a commutative algebra2007

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

      Publ. Math. Debrecen 70/3-4

      Pages: 453-460

    • Peer Reviewed
  • [Journal Article] On characterizations of the image of the Gelfand transform of commutative Banach algebras2007

    • Author(s)
      Jyunji Inoue and Sin-Ei Takahasi
    • Journal Title

      Math. Nachr. 280,No.1-2

      Pages: 105-126

    • Peer Reviewed
  • [Journal Article] Exponetial type functional equation and its Hyers-Ulam stability2007

    • Author(s)
      Sin-Ei Takahasi, Takeshi, Miura and Hiroyuki Takagi
    • Journal Title

      J. Math. Anal. Appl. 329

      Pages: 1191-1203

    • Peer Reviewed
  • [Journal Article] On Wirtinger's inequality and its elementary proof2007

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

      J. Math. Anal. Appl. 10

      Pages: 311-319

    • Peer Reviewed
  • [Journal Article] Hyers-Ulam stability of the first order linear differential equation for Banach space-valued holomorphic mappings2007

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

      Banach J. Math. Anal. 1-1

      Pages: 125-130

    • Peer Reviewed
  • [Journal Article] Refined generalization of the triangle inequality on Banach space

    • Author(s)
      Sin-Ei Takahasi, John M. Rassias, Saburou Saitoh and Yasuji Takahashi
    • Journal Title

      Math. Inequal. AppL (in press)

    • Peer Reviewed
  • [Journal Article] A general Hlawka inequality and its reverse inequality

    • Author(s)
      Yasuji Takahashi, Shuhei Wada and Sin-Ei Takahasi
    • Journal Title

      Math. Inequal. Appl. (in press)

    • Peer Reviewed
  • [Journal Article] A perturbation of first order linear differential equation for Banach space-valued holomorphic functions

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

      J. Math. Inequal. (in press)

    • Peer Reviewed
  • [Journal Article] A perturbation of normal operators on a Hilbert space

    • Author(s)
      Takeshi Miura, Atsushi Uchiyama, Hirokazu Oka, Go Hirasawa, Sin-Ei Takahasi and Norio Niwa
    • Journal Title

      Nonlinear Funct. Anal. Appl. (in press)

    • Peer Reviewed
  • [Journal Article] A Cauchy-Euler type factorization of operators

    • Author(s)
      Sin-Ei Takahasi, Hirokazu Oka, Takeshi Miura and Hiroyuki Takagi
    • Journal Title

      Tokyo J. Math. (in press)

    • Peer Reviewed
  • [Journal Article] On surjective ring homomorphisms between semi-simple commutative Banachalgebras

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

      Publ. Math. Debrecen. (in press)

    • Peer Reviewed
  • [Journal Article] Ger type stability of the first order linear differential equation y'(t)=h(t)y(t)

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

      Tamsui Oxf J. Math. Sci. (in press)

    • Peer Reviewed
  • [Presentation] 可換Banach環を知ろう2008

    • Author(s)
      高橋眞映
    • Organizer
      日本数学会(春季:企画特別講演)
    • Place of Presentation
      近畿大学本部キャンパス
    • Year and Date
      2008-03-25
  • [Presentation] Banach環のunitization上のnormに関する話し2007

    • Author(s)
      高橋眞映、三浦 毅
    • Organizer
      実解析学シンポジウム2007
    • Place of Presentation
      大阪教育大学天王寺キャンパス
    • Year and Date
      2007-10-21

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Published: 2010-02-04   Modified: 2016-04-21  

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