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Operator algebras and noncommutative analysis

Research Project

Project/Area Number 19540214
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionKyoto University

Principal Investigator

IZUMI Masaki  Kyoto University, 大学院・理学研究科, 教授 (80232362)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords作用素環 / 半群 / 正準交換関係 / 正準反交換関係 / Hardy空間 / Toeplitz作用素 / 生成作用素 / 群作用 / テンソル圏 / K-理論
Research Abstract

Operators on a Hilbert space, a generalization of the Euclid space, play fundamental roles in analysis and quantum physics. The set of bounded operators B(H) on a Hilbert space H is closed under linear operations, product, and conjugation, and it is a typical example of an operator algebra. In this research, I performed structure analysis of operator algebras. In particular, I studied the structure of a 1-parameter semigroup of endomorphisms of B(H), and obtained new classification invariants and construction of new examples.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (22 results)

All 2010 2009 2008 2007

All Journal Article (10 results) (of which Peer Reviewed: 10 results) Presentation (12 results)

  • [Journal Article] Toeplitz CAR flows and type I factorizations2010

    • Author(s)
      Masaki Izumi, R. Srinivasan
    • Journal Title

      Kyoto Journal of Mathematics Vol.50,no.1

      Pages: 1-32

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Toeplitz CAR flows and type I factorizations2010

    • Author(s)
      Masaki Izumi, R.Srinivasan
    • Journal Title

      Kyoto Journal of Mathematics 50

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Every sum system is divisible2009

    • Author(s)
      Masaki Izumi
    • Journal Title

      Transactions of American Mathematical Society Vol.361,No.8

      Pages: 4247-4267

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Every sum system is divisible2009

    • Author(s)
      Masaki Izumi
    • Journal Title

      Trans.Amer.Math.Soc. 361

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized CCR flows2008

    • Author(s)
      Masaki Izumi, R. Srinivasan
    • Journal Title

      Communications in Mathematical Physics Vol.281,No.2

      Pages: 529-571

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Classification of noncommuting quadrilateral of factors2008

    • Author(s)
      Pinhas Grossman, Masaki Izumi
    • Journal Title

      International Journal of Mathematics Vol.19,no.5

      Pages: 557-643

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Classification of noncommuting quadrilaterals of factors2008

    • Author(s)
      Pihas Grossman, Masaki Izumi
    • Journal Title

      International Journal of Mathematics 19

      Pages: 557-643

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized CCR flows2008

    • Author(s)
      Masaki Izumi, R. Srinivasan
    • Journal Title

      Communications in Mathematical Physics(電子版は既に掲載済み) (掲載予定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A perturbation problem for the shift semigroup2007

    • Author(s)
      Masaki Izumi
    • Journal Title

      Journal of functional analysis Vol.251,No.2

      Pages: 498-545

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A perturbation problem for the shift semigroup2007

    • Author(s)
      Masaki Izumi
    • Journal Title

      Journal of Functional Analysis 251

      Pages: 498-545

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Group actions on Kirchberg algebras2009

    • Author(s)
      Masaki Izumi
    • Organizer
      Asian mathematical conference
    • Place of Presentation
      プトラワールドトレードセンター, クアラルンプール, マレーシア
    • Year and Date
      2009-06-23
    • Related Report
      2009 Final Research Report
  • [Presentation] Group actions on Kirchberg algebras2009

    • Author(s)
      泉正己
    • Organizer
      第5回アジア数学会議
    • Place of Presentation
      クアラルンプール
    • Year and Date
      2009-06-23
    • Related Report
      2009 Annual Research Report
  • [Presentation] Mini-workshop "Product systems and independence in quantum dynamics"2009

    • Author(s)
      Masaki Izumi
    • Organizer
      Generalized CCR flows
    • Place of Presentation
      オーベルヴォルファッハ数学研究所, オーベルヴォルファッハ、ドイツ
    • Year and Date
      2009-02-18
    • Related Report
      2009 Final Research Report
  • [Presentation] Every sum system is divisible2008

    • Author(s)
      Masaki Izumi
    • Organizer
      作用素論作用素環論研究集会
    • Place of Presentation
      大阪教育大学
    • Year and Date
      2008-11-21
    • Related Report
      2009 Final Research Report
  • [Presentation] Workshop "von Neumann algebras and ergodic theory of group actions"2008

    • Author(s)
      Masaki Izumi
    • Organizer
      Generalized CCR flows
    • Place of Presentation
      オーベルヴォルファッハ数学研究所, オーベルヴォルファッハ, ドイツ
    • Year and Date
      2008-10-28
    • Related Report
      2009 Final Research Report
  • [Presentation] Classification of certain tensor categories2008

    • Author(s)
      泉正己
    • Organizer
      Operator Algebras, Conformal Field Theory and Related Topics
    • Place of Presentation
      シュレデインガー研究所
    • Year and Date
      2008-09-11
    • Related Report
      2008 Annual Research Report
  • [Presentation] Classification of certain tensor categories2008

    • Author(s)
      Masaki Izumi
    • Organizer
      Operator algebras, Conformal field theory and related topics
    • Place of Presentation
      シュレディンガー研究所, ウィーン, オーストリア
    • Year and Date
      2008-09-10
    • Related Report
      2009 Final Research Report
  • [Presentation] Group actions on Kirchberg algebras2008

    • Author(s)
      Masaki Izumi
    • Organizer
      First annual meeting of noncommutaive geometry network
    • Place of Presentation
      ダブリン上級研究所, ダブリン, アイルランド
    • Year and Date
      2008-06-18
    • Related Report
      2009 Final Research Report
  • [Presentation] Classification on Z2 actions on the Kirchberg algebras2007

    • Author(s)
      Masaki Izumi
    • Organizer
      Workshop on Structure of C*-algebras
    • Place of Presentation
      フィールズ研究所, トロント, カナダ
    • Year and Date
      2007-11-14
    • Related Report
      2009 Final Research Report
  • [Presentation] Quasi-free group actions on the Cuntz algebra O∞2007

    • Author(s)
      Masaki Izumi
    • Organizer
      京大数理解析研究所研究集会
    • Year and Date
      2007-09-12
    • Related Report
      2009 Final Research Report
  • [Presentation] Type III factors distinguish type III E0-semigroups2007

    • Author(s)
      Masaki Izumi
    • Organizer
      Workshop on noncommutative Dynamics and applications
    • Place of Presentation
      フィールズ研究所, トロント, カナダ
    • Year and Date
      2007-07-17
    • Related Report
      2009 Final Research Report
  • [Presentation] Type III factors distinguish type III EO-semigroups2007

    • Author(s)
      Masaki Izumi
    • Organizer
      Workshop on Noncommutative Dynamics and Applications
    • Place of Presentation
      The Field Institute, Toronto, Canada
    • Year and Date
      2007-07-17
    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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