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Research on the relative position of subspaces of a Hilbert space and operators

Research Project

Project/Area Number 23654053
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionKyushu University

Principal Investigator

WATATANI Yasuo  九州大学, 数理(科)学研究科(研究院), 教授 (00175077)

Co-Investigator(Renkei-kenkyūsha) ENOMOTO Masatoshi  甲子園大学, 総合教育研究機構 (70185130)
Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords関数解析 / ヒルベルト空間 / 部分空間の配置 / 直既約 / 拡大ディンキン図形 / 作用素 / quiver
Research Abstract

We study the relative position of n subspaces of a Hilbert space. It is important to consider indecomposable position. The case of n =1 and n =2 are solved. In finite dimensional Hilbert space, the case of n =3 and n =4 are solved and the indecomposable n subspaces are completely classified.
But infinite dimensional Hilbert space, even the case of n =3 and n =4 are still unsolved.
In our study, we attacked it by considering an analog of operator theory. We began to study Hilbert representations of quivers, which associate Hilbert spaces and operators for vertices and arrows of quivers. We investigate a complement in an infinite dimensional Hilbert space for Gabriel theorem using Dynkin diagrams A, D and E. We show that there exist infinite dimensional indecomposable Hilbert representations for extended Dynkin diagrams.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (19 results)

All 2015 2014 2013 2012 2011 2010 Other

All Journal Article (15 results) (of which Peer Reviewed: 14 results) Presentation (4 results) (of which Invited: 1 results)

  • [Journal Article] Perturbations of intermediate C*-subalgebras for simple C*-algebras2015

    • Author(s)
      S. Ino and Y. Watatani
    • Journal Title

      Bull. Lond. Math. Soc.

      Volume: 未定

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] C*-algebras associated with complex dynamical systems and backward orbit structure2014

    • Author(s)
      T. Kajiwara and Y. Watatani
    • Journal Title

      Complex anal. Oper. Theory

      Volume: 8 Pages: 243-254

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] C*-algebras associated with complex dynamical systems and backward orbit structure2014

    • Author(s)
      T. Kajiwara and Y. Watatani
    • Journal Title

      Complex anal. Oper. Theory

      Volume: 8 Pages: 243-254

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Traces on cores of C*-algebras associated with self-similar maps,2014

    • Author(s)
      T. Kajiwara and Y. Watatani
    • Journal Title

      Ergodic Theory Dynam. Systems.

      Volume: 未定

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] C*-algebras associated with complex dynamical systems and backward orbit structure2014

    • Author(s)
      T, Kajiwara and Y. Watatani
    • Journal Title

      Complex analysis and Operator theory

      Volume: 未定

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Traces on cores of C*-algebras associated with self-similar maps2014

    • Author(s)
      T. Kajiwara and Y. Watatani
    • Journal Title

      Ergodic Theory and Dynamical systems

      Volume: 未定

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] KMS states on finite graph C*-algebras2013

    • Author(s)
      T. Kajiwara and Y. Watatani
    • Journal Title

      Kyushu J. Math

      Volume: 67 Pages: 83-104

    • NAID

      130003364801

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] KMS states on finite graph C*-algebras2013

    • Author(s)
      T. Kajiwara and Y. Watatani
    • Journal Title

      Kyushu J. Math.

      Volume: 67 Pages: 83-104

    • NAID

      130003364801

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Fundamental group of simple C*-algebras with unique traceII2011

    • Author(s)
      N. Nawata and Y. Watatani
    • Journal Title

      J. Funct. Anal

      Volume: 260 Pages: 428-435

    • NAID

      120004951556

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] C*-algebras associated with algebraic correspondences on the Riemann sphere2011

    • Author(s)
      T. Kajiwara and Y. Watatani
    • Journal Title

      J. Operator Theory

      Volume: 65 Pages: 427-449

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Fundamental group of simple C*-algebras...2011

    • Author(s)
      Norio Nawata and Yasuo Watatani
    • Journal Title

      J. Funct. Anal.

      Volume: 260 Pages: 428-435

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] C*-algbras associated with algebraic correspon...2011

    • Author(s)
      Tsuyoshi Kajiwara and Yasuo Watatani
    • Journal Title

      J. Operator Theory

      Volume: 65 Pages: 427-449

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Traces on cores of C*-algebras associated with self-similar maps

    • Author(s)
      T. Kajiwara and Y. Watatani
    • Journal Title

      Ergodic Theory Dynam. Systems

      Volume: (to appear)

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Perturbations of intermediate C*-subalgebras for simple C*-algebras

    • Author(s)
      S. Ino and Y. Watatani
    • Journal Title

      Bull. Lond. Math. Soc

      Volume: (to appear)

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A construction on Hilbert representations of quivers

    • Author(s)
      M. Enomoto
    • Journal Title

      RIMS Kokyuroku

      Volume: (to appear)

    • Related Report
      2013 Final Research Report
  • [Presentation] Singularities in operator algebras2014

    • Author(s)
      綿谷安男
    • Organizer
      日本数学会年会
    • Place of Presentation
      学習院大学
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] C*-algebras generated by two operations2012

    • Author(s)
      Y. Watatani
    • Organizer
      MFO
    • Place of Presentation
      Oberwolfach, Germany
    • Related Report
      2013 Final Research Report
  • [Presentation] C*-algebras generated by two operations2012

    • Author(s)
      Y. Watatani
    • Organizer
      MFO
    • Place of Presentation
      オーバーヴォルバッハ数学研究所
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] 複素力学系から作られるC*-環とそのコア2010

    • Author(s)
      綿谷安男
    • Organizer
      作用素論作用素環論研究集会
    • Place of Presentation
      東京理科大
    • Related Report
      2013 Final Research Report

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Published: 2011-08-05   Modified: 2019-07-29  

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