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Studies of the Structure of Operators on Function Spaces

Research Project

Project/Area Number 10640189
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionNiigata Institute of Technology

Principal Investigator

WATANABE Seiji  Faculty of Engineering,Kanazawa Institute of Tecnology,Professor, 工学部, 教授 (40018271)

Co-Investigator(Kenkyū-buntansha) TAKENO Sigeharu  新潟工科大学, 工学部, 助教授 (30251789)
TANAKA Kensuke  新潟工科大学, 工学部, 教授 (70018258)
Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1999: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1998: ¥600,000 (Direct Cost: ¥600,000)
KeywordsFunction Spaces / Linear Operators / Unbounded Derivations / Weighted Compositi Operators
Research Abstract

The theory of function spaces plays an basic role in many branches of pure mathematics, for example, function analysis, differential equations, Fourier analysis, etc. and has become a useful tool in applied mathematics.
In this research, we studied the space of diffrentiable functions from the point of view of unbounded derivations.
The domain of a unbounded derivation in the space of continuous functions on a compact Hausdoruff space may be regarded as one of generalizations of the space of continuously differentiable functions. We investigated the structure of two important operators (that is, surjective linear isometries and small-bound isomorphisms) on such domain.
At first, we decided extreme points of the unit sphere of the conjugate space of the domain equipped with the Cambern norm and used it to prove that surjective linear isometries of the domain are weighted composition operators induced by homeomorphisms of the underlying compact Hausdorff spaces. When the underlying topological spaces satisfy the first countability axiom, this result is extended to the second order derivations.
We further studied small-bound isomorphisms on the domain and showed that if there is a small bound-isomorphism, then the underlying topological spaces are homeomorphic.
As by-product, we obtained Korovkin type approximation theorems on the space of continuously differentiable functions on the unit interval of the real line.

Report

(3 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • Research Products

    (11 results)

All Other

All Publications (11 results)

  • [Publications] Toshiko Matsumoto: "Surjective linear isometrics of the domain of a *-derivation equipped with the Cambern norm"Mathematische Zeitshrift. 230. 185-200 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Toshiko Matsumoto: "Small bound isomorphisms of the domain of a closed *-derivation"International Journal of Mathematics and Mathematical Applications. (in press).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Go Hirasawa: "Korovkin type approximation theorems on the space of continuously differentiable functions"Approximation theory and its applications. (in press).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Toshiko Matsumoto: "Surjective linear isometries of the domain of a*-derivation equipped with the Cambern norm"Mathematische Zeitshrift. 230. 185-200 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Toshiko Matsumoto: "Small bound isomorphisms of the domain of a closed *-derivation"International Journal of Mathematics and Mathematical Sciences. in press.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Go Hirasawa: "Korovkin type approximation theorems on the space of continuously differentiable functions"Approximation theory and its applications. in press.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] Toshiko Matsumoto: "Surjective linear isometries of the domain of a *-derivation equipped with the Cambern norm"Mathematische Zeitshrift. 230. 185-200 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Toshiko Matsumoto: "Small bound isomorphisms of the domain of a closed *-derivation"International Journal of Mathematics and Mathematical Sciences. (in press).

    • Related Report
      1999 Annual Research Report
  • [Publications] Go Hirasawa: "Korovkin type approximation theorems on the space of continuously differentiable functions"Approximation theory and its applications. (in press).

    • Related Report
      1999 Annual Research Report
  • [Publications] T.Matsumoto: "Suvjective linear isometries of the domain of a *-derivation equipped with the Cambern norm" Mathematische Zeitschrift. 230. 185-200 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Matsumoto: "Small bound isomorphisms of the domain of a closed *-derivation" International Journal of Math,and Math,Sci.(発表予定).

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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