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Study on von Neumann algebras, free probability and non-commutative function spaces

Research Project

Project/Area Number 24540214
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Global analysis
Research InstitutionKyushu University

Principal Investigator

UEDA Yoshimichi  九州大学, 数理(科)学研究科(研究院), 准教授 (00314724)

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsフォンノイマン環 / 自由積 / 軌道自由エントロピー / 前共役 / 自由確率論 / 情報量 / III型 / 非可換ハーディー空間 / 自由エントロピー / 非可換 L1-空間
Outline of Final Research Achievements

I clarified the structure of free product von Neumann algebras from various viewpoints. Especially, I identified the resulting free product von Neumann algebras with a certain explicit one under some conditions. Also, we computed several invariants for free product von Neumann algebras in the general setup, and obtained a result on the positional rigidity for subalgebras as well as a uniqueness result for the free product decomposition. I studied the orbital free entropy. In particular, we made some nontrivial computation of it. We also introduced the concept of pressure related to the orbital free entropy motivated by statistical physics and investigated its relation to random matrices. Moreover, I generalized the previous definition of orbital free entropy and discussed its general properties. Finally, we studied von Neumann algebra preduals and investigated a strong property, which is rather opposite to uniform convexity, for them.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (19 results)

All 2016 2015 2014 2013 Other

All Journal Article (7 results) (of which Peer Reviewed: 7 results,  Acknowledgement Compliant: 4 results,  Open Access: 1 results) Presentation (8 results) (of which Invited: 7 results) Remarks (4 results)

  • [Journal Article] Discrete cores of type III free product factors2016

    • Author(s)
      Yoshimichi Ueda
    • Journal Title

      Amer. J. Math.

      Volume: 138 Pages: 367-394

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Orbital free pressure and its Legendre transform2015

    • Author(s)
      F. Hiai and Y. Ueda
    • Journal Title

      Comm. Math. Phys.

      Volume: 334 Issue: 1 Pages: 275-300

    • DOI

      10.1007/s00220-014-2135-5

    • NAID

      120006714548

    • Related Report
      2015 Annual Research Report 2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Remarks on free mutual information and orbital free entropy2015

    • Author(s)
      Masaki Izumi, Yoshimichi Ueda
    • Journal Title

      Nagoya Math. J.

      Volume: 220 Pages: 45-66

    • DOI

      10.1215/00277630-3335530

    • NAID

      120006716057

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On the geometry of von Neumann algebra preduals2014

    • Author(s)
      Miguel Martin, Yoshimichi Ueda
    • Journal Title

      Positivity

      Volume: 18 Issue: 3 Pages: 519-530

    • DOI

      10.1007/s11117-013-0259-z

    • NAID

      120006714546

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Orbital free entropy, revisited2014

    • Author(s)
      Yoshimichi Ueda
    • Journal Title

      Indiana Univ. Math. J.

      Volume: 63 Issue: 2 Pages: 551-577

    • DOI

      10.1512/iumj.2014.63.5220

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Absence of Cartan subalgebras in continuous cores of free product von Neumann algebras2014

    • Author(s)
      Yoshimichi Ueda
    • Journal Title

      Proc. Japan Acad. Ser. A.

      Volume: 90 Issue: 10

    • DOI

      10.3792/pjaa.90.151

    • NAID

      40020331487

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Some analysis on amalgamated free products of von Neumann algebras in non-tracial setup2013

    • Author(s)
      Yoshimichi Ueda
    • Journal Title

      J. London Math. Soc.

      Volume: 88 Issue: 1 Pages: 25-48

    • DOI

      10.1112/jlms/jds081

    • Related Report
      2013 Research-status Report 2012 Research-status Report
    • Peer Reviewed
  • [Presentation] フォンノイマン環の自由積に関する総合報告2015

    • Author(s)
      植田 好道
    • Organizer
      作用素環の分類理論とその周辺
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-02-02 – 2015-02-04
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Discrete cores of type III free product factors2014

    • Author(s)
      Yoshimichi Ueda
    • Organizer
      作用素環論の最近の進展 (Recent Developments in Operator Algebras)
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-09-08 – 2014-09-10
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Orbital free entropy and its Legendre transform approach2014

    • Author(s)
      Yoshimichi Ueda
    • Organizer
      Free probability and the large N limit, IV
    • Place of Presentation
      Math. Dept., UC-Berkeley
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Free product von Neumann algebras with emphasis on structure theory for type III factors2013

    • Author(s)
      Yoshimichi Ueda
    • Organizer
      Workshop on Operator Algebras
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Orbital free entropy2013

    • Author(s)
      Yoshimichi Ueda
    • Organizer
      AMS-RMS joint meeting, Special session: Random matrices and free probability
    • Place of Presentation
      "1 Decembrie 1918" University of Alba Iulia, Romania
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Orbital free entropy and its dimension counterpart2013

    • Author(s)
      Yoshimichi Ueda
    • Organizer
      Workshop on analytic, stochastic, and operator algebraic aspects of noncommutative distributions and free probability in Focus program on noncommutative distributions in free probabilty
    • Place of Presentation
      Fields Institute
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 群,作用素環,そして確率2013

    • Author(s)
      植田 好道
    • Organizer
      日本数学会北海道支部講演会
    • Place of Presentation
      北海道大学理学研究院数学教室
    • Related Report
      2013 Research-status Report
  • [Presentation] Remarks on von Neumann algebra preduals

    • Author(s)
      植田 好道
    • Organizer
      RIMS 共同研究「量子化と作用素環」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Research-status Report
    • Invited
  • [Remarks] 植田の公表論文リスト

    • URL

      http://www2.math.kyushu-u.ac.jp/~ueda/publ.html

    • Related Report
      2015 Annual Research Report
  • [Remarks] Yoshimichi Ueda's homepage

    • URL

      http://www2.math.kyushu-u.ac.jp/~ueda/index.html

    • Related Report
      2014 Research-status Report
  • [Remarks] Publications by Y. UEDA

    • URL

      http://www2.math.kyushu-u.ac.jp/~ueda/publ.html

    • Related Report
      2013 Research-status Report
  • [Remarks] 自身のホームページ(Publication list)

    • URL

      http://www2.math.kyushu-u.ac.jp/~ueda/publ.html

    • Related Report
      2012 Research-status Report

URL: 

Published: 2013-05-31   Modified: 2019-07-29  

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