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Relative entropy for pairs of subalgebras and invariants arising from automorphisms

Research Project

Project/Area Number 20540209
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

CHODA Marie  Osaka Kyoiku University, 名誉教授 (80030378)

Co-Investigator(Kenkyū-buntansha) OKAYASU Rui  大阪教育大学, 教育学部, 准教授 (70362746)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords作用素環 / 非可換エントロピー / 自己同型写像 / エントロピー / 共役類 / 非可換力学系 / 接合積 / 因子環 / 相対エントロピー / エルゴート変換 / 群 / 状態 / エルゴード変換
Research Abstract

For a pair {A, B} of subalgebra of an operator algebra M, by modifying the Connes-Stormer relative entropy H(A|B), we defined h(A|B), and measured of distance between two algebras. For examples, in the case where M is the matrix algebra with the size n, then { h(A,B) ; A and B are maximal abelian subalgebras M}=[0.log n] and h(A,B)=log n iff A and B are mutually orthogonal. Similar result holds for pairs of subfactor with index 2 of type II_1 factors.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (34 results)

All 2011 2010 2009 2008 Other

All Journal Article (16 results) (of which Peer Reviewed: 11 results) Presentation (18 results)

  • [Journal Article] Conjugate Pairs of Subfactors and Entropy for Automorphisms2011

    • Author(s)
      Marie Choda
    • Journal Title

      International Journal of Mathematics 22巻

      Pages: 577-592

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 直交する場合、そして、その場合にのみ、最大になる値2011

    • Author(s)
      長田まりゑ
    • Journal Title

      国際数理科学協会会報 73巻

      Pages: 2-14

    • Related Report
      2010 Final Research Report
  • [Journal Article] Conjugate Pairs of Subfactors and Entropy for Automorphisms2011

    • Author(s)
      Marie Choda
    • Journal Title

      International Journal of Mathematics

      Volume: 22 Pages: 577-592

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Entropy for a Pair of Subalgebras via Automorphisms2010

    • Author(s)
      Marie Choda
    • Journal Title

      Bull.Malays.Math.Sci.Soc. 33巻

      Pages: 369-384

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Entropy for C*-algebras with tracial rank zero2010

    • Author(s)
      Rui Okayasu
    • Journal Title

      Proc.Amer.Math.Soc. no.10(138)

      Pages: 3609-3621

    • Related Report
      2010 Final Research Report
  • [Journal Article] Relative entropy for abelian subalgebras2010

    • Author(s)
      Rui Okayasu
    • Journal Title

      Internat J.Math. no.4(21)

      Pages: 537-550

    • Related Report
      2010 Final Research Report
  • [Journal Article] Entropy for a Pair of Subalgebras via Automorphisms2010

    • Author(s)
      Marie Choda
    • Journal Title

      Bull.Malays.Math.Sci.Soc.

      Volume: 33 Pages: 369-384

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Entropy for C-algebras with tracial rank zero2010

    • Author(s)
      Rui Okayasu
    • Journal Title

      Proc.Amer.Math.Soc.

      Volume: 138 Pages: 3609-3621

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Entropy for a pair of subalgebras via automorphisms2010

    • Author(s)
      Marie Choda
    • Journal Title

      Bull.Malays.Math.Sci.Soc.(2) (印刷中)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Relative Entropy for Conjugate Pairs of Subalgebras2009

    • Author(s)
      Marie Choda
    • Journal Title

      Proceedings of the workshop on Operator Theory and Operator Algebras

      Pages: 66-75

    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Journal Article] Relative entropy for maximal abelian subalgebras of matrices and the entropy of unistochastic matrices2008

    • Author(s)
      Marie Choda
    • Journal Title

      International Journal of Mathematics 19巻

      Pages: 767-776

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The ratio set of the harmonic measure of a random walk on a hyperbolic group2008

    • Author(s)
      Masaki Izumi, Sergey Nesyaveyev, Rui Okayasu
    • Journal Title

      Israel J.Math. 163巻

      Pages: 285-316

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Relative entropy for maximal abelian subalgebras of matricesis the entropy of unistochastic matrices2008

    • Author(s)
      Marie Choda
    • Journal Title

      International Journal of Mathematics 1 9

      Pages: 767-776

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The ratio set of the harmonic measure of a random walk on a hyperbolic group2008

    • Author(s)
      Masaki Izumi
    • Journal Title

      Israel J. Math 163

      Pages: 285-316

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Entropy via partitions of unity

    • Author(s)
      長田まりゑ
    • Journal Title

      京都大学数理解析研究所講究録 印刷中

    • Related Report
      2010 Final Research Report
  • [Journal Article] Relative entropy for abelian subalgebras

    • Author(s)
      Rui Okayasu
    • Journal Title

      Internat.J.Math. (印刷中)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] Tracial topological approximation entropy2011

    • Author(s)
      岡安類
    • Organizer
      Weekly seminar
    • Place of Presentation
      Centre de Recerca Matematica (Spain)
    • Related Report
      2010 Final Research Report
  • [Presentation] On the Toeplitz algebras of quasi-lattice ordered groups2011

    • Author(s)
      岡安類
    • Organizer
      研究集会「作用素環の対称性の研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2010 Final Research Report
  • [Presentation] Entropy via partitions of unity2010

    • Author(s)
      Marie Choda
    • Organizer
      RIMS研究集会:独立性と従属性の数理-函数解析学の視点から-
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-12-22
    • Related Report
      2010 Final Research Report
  • [Presentation] Tracial topological approximation entropy2010

    • Author(s)
      岡安類
    • Organizer
      作用素論・作用素環論研究集会
    • Place of Presentation
      東京理科大学森戸記念館
    • Year and Date
      2010-11-15
    • Related Report
      2010 Final Research Report
  • [Presentation] どこを問題にして、違いを表す数値を導き出すか2010

    • Author(s)
      長田まりゑ
    • Organizer
      公開講座
    • Place of Presentation
      賢明女子学園中学・高等学部姫路市
    • Year and Date
      2010-11-13
    • Related Report
      2010 Final Research Report
  • [Presentation] Positive definite matrices arising from unitaries2010

    • Author(s)
      Marie Choda
    • Organizer
      13th WORKSHOP : NON-COMMUTATIVE HARMONIC ANALYSIS WITH APPLICATIONS TO PROBABILITY
    • Place of Presentation
      Bedlewo, Poland
    • Year and Date
      2010-07-14
    • Related Report
      2010 Final Research Report
  • [Presentation] Positive definite matrices arising from unitaries2010

    • Author(s)
      Marie Choda
    • Organizer
      13th Workshop : Non-commutative harkmonic analysis with applications to probability
    • Place of Presentation
      Bedlewo, Poland
    • Year and Date
      2010-07-14
    • Related Report
      2010 Annual Research Report
  • [Presentation] Unitary operators and pairs of subalgebras2010

    • Author(s)
      Marie Choda
    • Organizer
      2010 KOTAC International Conference : Operator Theory and Its Applications
    • Place of Presentation
      University of Incheon, Korea
    • Year and Date
      2010-06-17
    • Related Report
      2010 Final Research Report
  • [Presentation] Relative Entropy for Conjugate Pairs of Subalgebras2009

    • Author(s)
      Marie Choda
    • Organizer
      「作用素論・作用素環論」研究集会
    • Place of Presentation
      奈良教育大学
    • Year and Date
      2009-11-19
    • Related Report
      2010 Final Research Report
  • [Presentation] Entropy for inner conjugacy class of subalgebras2009

    • Author(s)
      Marie Choda
    • Organizer
      The 9th Sendai Workshop on Infinite Dimensional Analysis and Quantum Probability
    • Place of Presentation
      東北大学
    • Year and Date
      2009-09-11
    • Related Report
      2010 Final Research Report
  • [Presentation] Entropy on matrix algebras2009

    • Author(s)
      Marie Choda
    • Organizer
      ESI Seminar, The Erwin Schrodinger International Institute for Mathematical
    • Place of Presentation
      Physics
    • Year and Date
      2009-09-03
    • Related Report
      2010 Final Research Report
  • [Presentation] 二つの部分環の間の隔たりを測る量について2009

    • Author(s)
      Marie Choda
    • Organizer
      「関数解析学の研究とその応用」研究集会
    • Place of Presentation
      クロスパル新潟
    • Year and Date
      2009-08-28
    • Related Report
      2010 Final Research Report
  • [Presentation] Fourier expansions and inner conjugacy class of subfactors2009

    • Author(s)
      Marie Choda
    • Organizer
      12th WORKSHOP : NON-COMMUTATIVE HARMONIC ANALYSIS WITH APPLICATIONS TO PROBABILITY
    • Place of Presentation
      Bedlewo, Poland
    • Year and Date
      2009-08-18
    • Related Report
      2010 Final Research Report
  • [Presentation] Entropy for a pair of subalgebras arising from automorphisms2009

    • Author(s)
      Marie Choda
    • Organizer
      Operator Algebra Special Session AMC-2009
    • Place of Presentation
      PWTC Kuala Lumpur Malaysia
    • Year and Date
      2009-06-24
    • Related Report
      2010 Final Research Report
  • [Presentation] Entropy for a pair of subalgebras arising from automorphisms2009

    • Author(s)
      Marie Choda
    • Organizer
      AMC(Asian Mathematical Conference)-2009
    • Place of Presentation
      PWTC Kuala Lumpur Malaysia
    • Year and Date
      2009-06-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] Entropies for two subalgebras of operator algebras2008

    • Author(s)
      Marie Choda
    • Organizer
      Information and Communication Conference
    • Place of Presentation
      Alfred Renyi Institute of Mathematics, Budapest, Hungary
    • Year and Date
      2008-08-27
    • Related Report
      2010 Final Research Report
  • [Presentation] Entropies for two subalgebras of operator algebras2008

    • Author(s)
      Marie Choda
    • Organizer
      Information and Communi cat ion Conference
    • Place of Presentation
      ハンガリー(Alfred Renyi Institute of Mathematics)
    • Year and Date
      2008-08-27
    • Related Report
      2008 Annual Research Report
  • [Presentation] Relative entropy for finite dimensional abelian subalgebras2008

    • Author(s)
      岡安類
    • Organizer
      日本数学会函数解析学分科会
    • Place of Presentation
      東京工業大学
    • Related Report
      2010 Final Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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