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On the interplay between C^*-algebras and topological dynamical systems

Research Project

Project/Area Number 09640226
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field 解析学
Research InstitutionJapan Women's University

Principal Investigator

TOMIYAMA Jun  Japan Women's Univ., Fac.of Sci., Professor, 理学部, 教授 (30006928)

Co-Investigator(Kenkyū-buntansha) MINEMURA Katsuhiro  Japan Women's Univ., Fac.of Sci., Prefessor, 理学部, 教授 (20060684)
FUJISAKI Rieko  Japan Women's Univ., Fac.of Sci., Prefessor, 理学部, 教授 (30060635)
OEDA Kazuo  Japan Women's Univ., Fac.of Sci., Prefessor, 理学部, 教授 (10060675)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1998: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1997: ¥1,500,000 (Direct Cost: ¥1,500,000)
KeywordsC^*-algebra / Topological dynamical system / Elementary sets of dynamical system / Orbit equivalence / Heat convection equation / Foliation / C^*-環 / C^* 環 / 充足群
Research Abstract

The followings are main points of our results during the academic years through 1997 to 1998(Heisei 9-10). Among them, the first four items are carried out by Tomiyama.
1.Proved the restricted isomorphism theorem for the best possible wide classes of dynamical systems ; namely obtained the condition between dynamical systems when their associated C-algebras are isomorphic keeping the subalgebras of continuous functions for such a class.
2.Introduced the representation theory of dynamical systems as a new stand pointof the theory As consequences, we have reinforced the previous results in this field.
3.Cultivated various kinds of ways to attack the general isomorphism problem, among which one is the idea of universal C-Z-crossed product with its analysis andthe other is to distinguish the ideal of homeomorphism C-algebras as good and bad (and most bad) ones together with the characterizations of good ideals. Also analysed the properties of isomophisms from this point.
4.Obtained the C-algebraic descriptions of the behavior of nonwandering sets ofdynamical systems, the depths of the Birkhoff center. Among those elementary sets of dynamical systems, only this thing had been remained unsolved for several years.
5.Qeda has obtained the global solutions for the initial value problem of the heat convection equation in an exterior domain in the 2 or 3 dimensional Eucidean spaces. For a codimension q Hausdorff foliation having Torus as general leaves in the 4 or 5 dimensional compact manifold, Fujisaki has classified the types of singular leaves with the analysis of their local stabilities.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (17 results)

All Other

All Publications (17 results)

  • [Publications] 富山 淳: "Bounded topological orbit equivalence and C^*-algebras" Journal of Mathematical Society of Japan. 50-2. 317-329 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 富山 淳: "Pepresentations of topological dynamical systems and C^*-algebras" Conptemporary Mathematics. 228. 351-364 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 大枝 一男: "Initial value problems for the heat convection equations in exterior domains" Tokyo Journal of Mathematics. 21-2. 359-375 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 藤崎 リエ子: "Stability of singular leaves of compact Hausdorff foliations with tori as generic leaves" Tokyo Journal of Mathematics. (予定).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Tomiyama: "Bounded topological orbit equivalence and C^*-algebras" Journal of Mathematical Society of Japan. 50-2. 317-329 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] J.Tomiyama: "Representations of topological dynamical systems and C^*-algebras" Contemporary Mathematics. 228. 351-364 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Oeda: "Initial value problems for the heat convection equations in exterior domains" Tokyo Journal of Mathematics. 21-22. 359-375 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] R.Fujisaki: "Stability of singular leaves of compact Hausdorff foliations with tori as generic leaves" Tokyo Journal of Mathematics. (To appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] 富山 淳: "Bounded topological orbit equivalence and C^*-algebras" Journal of Mathematical Society of Japan. 50-2. 317-329 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 富山 淳: "Representations of topological dynamical systems and C^*-algebras" Conptemporary Mathematics. 228. 351-364 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] 大枝 一男: "Initial value problems for the heat convection equations in exterior domains" Tokyo Journal of Mathematics. 21-2. 359-375 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 藤崎 リエ子: "Stability of singular leaves of compact Hausdorff foliarions with tori as generic leaves" Tokyo Journal of Mathematics. (予定).

    • Related Report
      1998 Annual Research Report
  • [Publications] 富山 淳: "Representations of topological dynamical systems and C^*-algebras" Proc.Intern.Conf.″Operator algebras and operators theory″. (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 大枝 一男: "Periodic solutions of the heat convection equations in exterior domains" Proc.Japan Academy. 73(4). 49-54 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 大枝 一男: "Stationary solutions of the heat convection equations in exterior domains" Proc.Japan Academy. 73(6). 111-115 (1997)

    • Related Report
      1997 Annual Research Report
  • [Publications] 大枝 一男: "Asymptotic expansions of solutions of the penalized linear heat convection equations" 日本女子大学理学部紀要. 6. (1998)

    • Related Report
      1997 Annual Research Report
  • [Publications] 富山 淳: "Topologically free dynamical systems and operator algebras" Intern.Conf.″von Ncumann algebras and dynamical systems″. (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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