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

Theory and applications of functional analysis

Research Project

Project/Area Number 61540107
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 解析学
Research InstitutionOsaka University

Principal Investigator

TAKENOUCHI Osamu  Osaka University, faculty of engineering science, 基礎工学部, 教授 (20029375)

Co-Investigator(Kenkyū-buntansha) NAGISA Masaru  Osaka University, faculty of engineering science, 基礎工学部, 助手 (50189172)
HAYAKAWA Kantaro  Osaka University, faculty of engineering science, 基礎工学部, 講師 (10028201)
SHIRAHATA Shingo  Osaka University, faculty of engineering science, 基礎工学部, 助教授 (10037294)
KURISU Tadashi  Osaka University, faculty of engineering science, 基礎工学部, 助教授 (00029159)
SAKAGUCHI Minoru  Osaka Iniversity, faculty of engineering science, 基礎工学部, 教授 (70029388)
片山 良一  滋賀県立短期大学, 助教授 (10093395)
丘本 正  大阪大学, 基礎工学部, 教授 (80029389)
Project Period (FY) 1986 – 1987
Project Status Completed (Fiscal Year 1987)
Budget Amount *help
¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 1987: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1986: ¥800,000 (Direct Cost: ¥800,000)
KeywordsFunctional analysis / Operator algebras / Jones index / Relative entropy / Complete positive map C^ dynamical system / Bounded representation / 有界表現 / 微分(作用素環における) / 完全有界写像 / 接合積 / index / 相対エントロピー
Research Abstract

The theory of operator algebras was the principal subject of the present research.
(1) Jones index of subfactors of II_1 factors and the relative entropy of Pimsner and Popa. These have intimate relations to each other and also have close relations with the structure of the original factor. We investigated these interrelations, and special attentions were put in the case of a factor and its crossed product with a finite group when the group acted on the factor as a group of outer automorphisms.
(2) Completely positive maps among C^ algebras. The notion of homomorphism between C^ algebras is extended somehow as completely positive maps. This s an important notion in recent researches. Among ordered Banach spaces composed of bounded linlear operators between C^ algebras, this notion of completely positive maps can be introduced. Then a question : When does the mere assumption of the positivity imply the complete positiviey ? It was observed that, for the affirmative answer to this question, abelian characters of component C^ algebras play some roles.
(3) C^ dynamical system. Tesearches were made from the point of view of applications. The fixed subalgebra. The spectrum, i.e. the space of the irreducible representations. The lifting problem of a state of the original algebra to the crossed product. And so on.
(4) The so-called similarity problem, which asks if a bounded representation of a C^ algebra is equivalent to a ^ representation. It is related with the derivations and the norms of completely bounded maps. We determined these norms exactly when the C^ algebras in question were of finite dimension and made applications of this result to the general case.

Report

(2 results)
  • 1987 Final Research Report Summary
  • 1986 Annual Research Report
  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] 河上哲,吉田裕恋: J.Math.Soc.Japan. 39. 609-626 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] 楠田雅治: Mathematica Japonica. 32. 769-780 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] 渚勝,宋亀: Mathematica Japonica. 32. 801-810 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] 楠田雅治: Proc.Amer.Meth.Soc. 102. 90-94 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] S.Kawakami & H.Yosida: "Actions of finite groups on finite fon Neumann algebras and the relative entropy" J.Math. Soc. Japan. 39. 606-626 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] M.Kusuda: "G-primitive spectrum of a C^ algebra" Mathematica Japonica. 32. 769-789 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] M.Nagisa & G.Song: "On some property of bounded homomorphisms and derivations of a C algebra" Mathematica Japonica. 32. 801-810 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] M.Kusuda: "Hereditary C^ subalgebras of a C^ crossed product" Proc. Amer. Math. Soc.102. 90-94 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] 渚勝,宋亀: Mathematica Japonica. 32. (1987)

    • Related Report
      1986 Annual Research Report
  • [Publications] 伊藤隆: Mathematica Japonica. 31. 607-616 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] 楠田雅治: London Mathematical Society.

    • Related Report
      1986 Annual Research Report
  • [Publications] 吉田稔: Osaka Mathematical Journal. 23. 415-421 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] 坂口実: Mathematica Japonica. 32. 105-122 (1987)

    • Related Report
      1986 Annual Research Report
  • [Publications] 竹之内脩: "ベクトル解析" サイエンス社, 150 (1986)

    • Related Report
      1986 Annual Research Report

URL: 

Published: 1987-03-31   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi