• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

非有界作用素による可換Banach環の代数的及び位相的構造の研究

Research Project

Project/Area Number 15740082
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Basic analysis
Research InstitutionYamagata University

Principal Investigator

三浦 毅  山形大学, 工学部, 助教授 (90333989)

Project Period (FY) 2003 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2003: ¥1,400,000 (Direct Cost: ¥1,400,000)
Keywords可換Banach環 / 極大イデアル空間 / 非有界作用素 / 環準同型写像 / 微分作用素 / Hyers-Ulam stability
Research Abstract

まず微分作用素の安定性に関しては,微分方程式y'(t)+p(t)y(t)+q(t)=0を考え,この方程式に対応する微分作用素(Tf)(t)=f(t)+p(t)f(t)+q(t)がHyers-Ulam-Rassias stabilityをもつことを示した.この結果は既出のT.Miura, S.-M.Jung and S.-E.Takahasiの定理を一般化するとともに,さらにより簡単な証明によって示されることを述べた.さらに微分作用素よりも広い,Hilbert空間上の閉作用素に対しては,Hyers-Ulamの意味での安定性が成り立つための,いくつかの必要十分条件を与え,安定性に関する最良定数を決定した.この結果は既に知られている,Banach空間上の有界作用素がHyers-Ulamの意味で安定性を有するための必要十分条件が,空間をHilbert空間に限定すれば,実は非有界作用素に対してもそのまま安定性を特徴付ける条件になることを示している.Banach空間上の有界作用素に対しては,安定性の最良定数が存在しない例が知られている.したがって非有界作用素に対しても安定性の最良定数が存在することは期待できないが,Hilbert空間上の作用素であれば必ず最良定数が存在し,その定数がある種の逆写像の作用素ノルム,あるいはlower boundと呼ばれる既存の量と一致することも示した.一般の可換Banach環上には微分作用素を定義することは不可能であるが,derivationと呼ばれる微分作用素に対応する写像は古くから研究対象とされている.Derivationをさらに一般化したring derivationに対しては,より強い意味での安定性が成り立つことを示した.より正確に述べれば,近似的なring derivationは実はring derivationであることが分かったのである.言い換えればring derivationの摂動は本質的には存在し得ないのである.
さらに環準同型写像の構造に関連して,関数環上の同型写像をスペクトルで特徴付けることに成功した.この結果はMolnarの結果を大幅に拡張するものであるが,関連した結果も発表されていることから,世界的に注目を集めている研究分野であるといえる.その中で関数環上の結果を,さらに可換Banach環上の等距離同型写像の特徴づけにまで拡張することが出来た.これらの諸結果は,しかるべき雑誌に掲載済みもしくは掲載予定であるので,詳細については下記の研究発表欄を参照されたい.

Report

(3 results)
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (42 results)

All 2006 2005 2004 Other

All Journal Article (28 results) Publications (14 results)

  • [Journal Article] Hyers-Ulam stability of a closed operator in a Hilbert space2006

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

      Bull. Korean Math. Soc. 43

      Pages: 107-117

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On the first homology of the group of equivariant Lipschitz homeomorphisms2006

    • Author(s)
      Kojun Abe, Kazuhiko Fukui, Takeshi Miura
    • Journal Title

      J. Math. Soc. Japan. 58

      Pages: 1-15

    • NAID

      10017178257

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A note on the Pearce-Pecaric inequalities.2005

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

      Sci. Math. Jpn. 61

      Pages: 99-107

    • NAID

      10014491776

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach Algebras2005

    • Author(s)
      Takeshi Miura, Sin-Ei Takahasi, Go Hirasawa
    • Journal Title

      J. Inequal. Appl. 2005:4

      Pages: 435-441

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Convergency of a recursive sequence X_<n+1>=(βX_<n-1>)/{1+α(X_<n-1>+X_n)} and its application to a model for competing species2005

    • Author(s)
      Yasuhide Miura, Sin-Ei Takahasi, Takeshi Miura, Makoto Tsukada
    • Journal Title

      J. Anal. Appl 3

      Pages: 205-222

    • Related Report
      2005 Annual Research Report
  • [Journal Article] The Hyers-Ulam-Rassias stability of differential operators and its applications2005

    • Author(s)
      Takeshi Miura
    • Journal Title

      Nonlinear Funct. Anal. Appl. 10

      Pages: 535-553

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Averaging functions and inequalities due to Holder-Rogers and Minkowski2005

    • Author(s)
      Sin-Ei Takahasi, Takeshi Miura, Kunio Sato
    • Journal Title

      Sci. Math. Jpn. 62

      Pages: 289-298

    • NAID

      10020542857

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A reconsideration of Hua's inequality,2005

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

      J. Inequal. Appl. 2005:1

      Pages: 15-23

    • Related Report
      2005 Annual Research Report
  • [Journal Article] The Hyers-Ulam stability of a weighted composition operator on a uniform algebra2004

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

      Journal of Nonlinear and Convex Analysis 5

      Pages: 43-48

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Ger type and Hyers-Ulam stabilities for the first order linear differential operators of entire functions2004

    • Author(s)
      Takeshi Miura, Go Hirasawa, Sin-Ei Takahasi
    • Journal Title

      International Journal of Mathematics And Mathematical Sciences 22

      Pages: 1151-1158

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The Hyers-Ulam stability constants of first order linear differential operators2004

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

      Journal of Mathematical Analysis and Applications 296

      Pages: 403-409

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A note on commutative Gelfand theory for real Banach algebras2004

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

      Mathematical Journal of Okayama University 46

      Pages: 121-129

    • NAID

      120002309904

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations y'=λy2004

    • Author(s)
      Takeshi Miura, Soon-Mo Jung, Sin-Ei Takahasi
    • Journal Title

      Journal of Korean Mathematical Society 41

      Pages: 995-1005

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Stability of multipliers on Banach algebras2004

    • Author(s)
      Takeshi Miura, Go Hirasawa, Sin-Ei Takahasi
    • Journal Title

      International Journal of Mathematics And Mathematical Sciences 45

      Pages: 2377-2381

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On the best constant of Hyers-Ulam stability2004

    • Author(s)
      O.Hatori, K.Kobayashi, H.Takagi, T.Miura, S.-E.Takahasi
    • Journal Title

      Journal of Nonlinear and Convex Analysis 5

      Pages: 387-393

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A note on the Pearce-Pecaric inequalities2004

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

      Scientiae Mathematicae Japonicae 61

      Pages: 99-107

    • NAID

      10014491776

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On convergency of a recursive sequence x_<n+1>=f(X_<n_1>,x_n)

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

      Taiwanese Journal of Mathematics 近刊

    • Related Report
      2005 Annual Research Report
  • [Journal Article] A perturbation of ring derivations on Banach algebras

    • Author(s)
      Takeshi Miura, Go Hirasawa, Sin-Ei Takahasi
    • Journal Title

      J. Math. Anal. Appl. 近刊

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Characterizations of isometric isomorphismsbetween uniform algebras via non-linear range preserving properties

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

      Proc. Amer. Math. Soc. 近刊

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Note on the Hyers-Ulam-Rassias stability of the first order linear differential equation y'(t)+p(t)y(t)+q(t)=0

    • Author(s)
      Takeshi Miura, Go Hirasawa, Sin-Ei Takahasi
    • Journal Title

      Nonlinear Funct. Anal. Appl. 近刊

    • Related Report
      2005 Annual Research Report
  • [Journal Article] On Wirtinger's inequality and its elementary proof

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

      J. Funct. Spaces Appl. 近刊

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Prime ideals and complex ring homomorphisms on a commutative algebra

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

      Publ. Math. 近刊

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Spectra preserving maps between commutative Banach algebras

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

      J. Math. Anal. Appl. 近刊

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach Algebras

    • Author(s)
      Takeshi Miura, Sin-Ei Takahasi, Go Hirasawa
    • Journal Title

      Journal of Inequalities and Applications 近刊

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On convergency of a recursive sequence x_<n+1>=f(x_<n-1>,x_n)

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

      Taiwanese Journal of Mathematics 近刊

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A reconsideration of Hua's inequality

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

      Journal of Inequalities and Applications 近刊

    • Related Report
      2004 Annual Research Report
  • [Journal Article] The Hyers-Ulam-Rassias stability of differential operators and its applications

    • Author(s)
      Takeshi Miura
    • Journal Title

      Nonlinear Functional Analysis and Applications 近刊

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Convergency of a Recursive sequence x_<n+1>=βx_<n-1>/{1+α(x_<n-1>+x_n)} and its application to a model for competing species

    • Author(s)
      Yasuhide Miura, Sin-Ei Takahasi, Takeshi Miura, Makoto Tsukada
    • Journal Title

      Journal of Analysis and Applications 近刊

    • Related Report
      2004 Annual Research Report
  • [Publications] S.-E.Takahasi, T.Miura: "A note on Wirtinger-Beesack's integral inequalities"Mathematical Inequalities & Applications. 6. 277-282 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] S.-E.Takahasi, H.Oka, T.Miura: "On the structure of a third kind boundary value problem"Mathematische Nachrichten. 257. 99-107 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Miura, K.Niijima: "On a characterization of the maximal ideal spaces of algebraically closed commutative C^*-algebras"Proceedings of the American Mathematical Society. 131. 2869-2876 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Miura, S.Miyajima, S.-E.Takahasi: "Hyers-Ulam stability of linear differential operator with constant coefficients"Mathematische Nachrichten. 258. 90-96 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] O.Hatori, T.Ishii, T.Miura, S.-E.Takahasi: "Characterizations and automatic linearity for ring homomorphisms on algebras of functions"Contemporary Mathematics. 328. 201-215 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Miura, S.-E.Takahasi: "Ring homomorphisms on real Banach algebras"International Journal of Mathematics and Mathematical Sciences. 48. 3025-3030 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Miura, S.Miyajima, S.-E.Takahasi: "A characterization of Hyers-Ulam stability of first order linear differential operator"Journal of Mathematical Analysis and Applications. 286. 136-146 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Takagi, T.Miura, S.-E.Takahasi: "Essential norm and stability constant of weighted composition operators on C(X)"Bulletin of the Korean Mathematical Society. 40. 583-591 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Miura, G.Hirasawa, S.-E.Takahasi: "Ger type and Hyers-Ulam stabilities for the first order linear differential operators of entire functions"International Journal of Mathematics and Mathematical Sciences. 近刊.

    • Related Report
      2003 Annual Research Report
  • [Publications] H.Takagi, T.Miura, S.-E.Takahasi: "The Hyers-Ulam stability of a weighted composition operator on a uniform algebra"Journal of Nonlinear and Convex Analysis. 近刊.

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Miura, S.M.Jung, S.-E.Takahasi: "Hyers-Ulam-Rassias stability of the Banach space valued linear differential equations y'=λy"Journal of Korean Mathematical Society. 近刊.

    • Related Report
      2003 Annual Research Report
  • [Publications] S.-E.Takahasi, T.Miura, O.Hatori: "A note on commutative Gelfand theory for real Banach algebras"Mathematical Journal of Okayama University. 近刊.

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Miura, S.-E.Takahasi, G.Hirasawa: "Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras"Archives of Inequalities and Applications. 近刊.

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Miura, G.Hirasawa, S.-E.Takahasi: "Stability of multipliers on Banach algebras"International Journal of Mathematics and Mathematical Sciences. 近刊.

    • Related Report
      2003 Annual Research Report

URL: 

Published: 2003-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi