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Study on permenent properties for inclusion of C*-algebras

Research Project

Project/Area Number 26400125
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionRitsumeikan University

Principal Investigator

Osaka Hiroyuki  立命館大学, 理工学部, 教授 (00244286)

Co-Investigator(Renkei-kenkyūsha) TERUYA TAMOTSU  群馬大学, 教育学部, 教授 (30594246)
Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
KeywordsRokhlin property / Cuntz-Pimsner algebras / Hilbert C*-modules / Nuclear dimension / Self-absorbing / Cuntz semigroups / Hilbert C*-module / Jiang-Su algebra / Strict comparison / Linking algebras / C*-環 / C*-指数理論 / ロホリン性 / Pimsner-Popa 不等式 / Jiang-Su 環
Outline of Final Research Achievements

Throgh the joint work with Prof. Teruya we formulated the Rokhlin property for inclusion of nonunital C*-algebras with a index finite related to the Pimsner-Popa inequlity, using the sequentially *-homomorphism by Balak-Szabo, and we showed the stability for permanence properties for inclusion of C*-algebras. Also, we defined the Rokhlin property for actions of finite groups on Hilbert C*-modules, and studied its basic properties.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (30 results)

All 2017 2016 2015 2014 Other

All Int'l Joint Research (3 results) Journal Article (8 results) (of which Int'l Joint Research: 7 results,  Peer Reviewed: 8 results,  Open Access: 8 results,  Acknowledgement Compliant: 4 results) Presentation (16 results) (of which Int'l Joint Research: 8 results,  Invited: 11 results) Remarks (3 results)

  • [Int'l Joint Research] IIT Bombay/IIT Hyderabad(インド)

    • Related Report
      2016 Annual Research Report
  • [Int'l Joint Research] Indian Institute of Technology Bombay(India)

    • Related Report
      2015 Research-status Report
  • [Int'l Joint Research] Mathematical Institute/Institute for computational Sciences(ベトナム)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Permanence of nuclear dimension for inclusions of unital C*-algebras with the Rokhlin property2017

    • Author(s)
      H. Osaka and T. Teruya
    • Journal Title

      Advances in Operator Theory

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] The generalized reverse Cauchy inequality2016

    • Author(s)
      D. T. Hoa, T. B. Khue, and H. Osaka
    • Journal Title

      Linear and Multilinear Algebras

      Volume: 64 Issue: 7 Pages: 1415-1423

    • DOI

      10.1080/03081087.2015.1087459

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Matrix monotone functions and the generalized Powers-Stormer inequality2016

    • Author(s)
      H. Osaka
    • Journal Title

      Ordered Structures and Applications: Positivity VII Trends in Mathematics

      Volume: - Pages: 349-361

    • DOI

      10.1007/978-3-319-27842-1_22

    • ISBN
      9783319278407, 9783319278421
    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Unexpected relations which characterize operator means2016

    • Author(s)
      H. Osaka and S. Wada
    • Journal Title

      Proceedings of the Amerian Mathematical Society, Series B

      Volume: 3 Pages: 9-17

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Inequalities for interpolation functions2015

    • Author(s)
      Dinh Trung Hoa and H. Osaka
    • Journal Title

      Banach J. Math. Anal.

      Volume: 9 Pages: 67-74

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Interpolation classes and matrix means2015

    • Author(s)
      Dinh Trung Hoa, Toan M. Ho, and H. Osaka
    • Journal Title

      Banach J. Math. Anal.

      Volume: 9 Pages: 140-152

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Characterization of operator monotone functions by Powers-Størmer type inequalities2015

    • Author(s)
      Dinh Trung Hoa, H. Osaka, and J. Tomiyama
    • Journal Title

      Linear Multilinear Algebras

      Volume: 63 Pages: 1577-1589

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Strongly self-absorbing property for inclusions of C*-algebras with a finite Watatani index2014

    • Author(s)
      H. Osaka and T. Teruya
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: 366 Pages: 1685-1702

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] Matrix functions, matrix means, matrix inequalities2016

    • Author(s)
      H. Osaka
    • Organizer
      Recent advances in Operator Theory and Operator Algebras2016
    • Place of Presentation
      (インド)バンガロール
    • Year and Date
      2016-12-19
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Generalized reverse Cauchy inequality and applications to operator means2016

    • Author(s)
      H. Osaka, Y. Tsurumi, S. Wada
    • Organizer
      日本数学会2016年度秋期総合分科会
    • Place of Presentation
      (東京都八王子市)首都大学
    • Year and Date
      2016-09-16
    • Related Report
      2016 Annual Research Report
  • [Presentation] The Rokhlin property for group actions on Hilbert C*-modules2016

    • Author(s)
      H. Osaka
    • Organizer
      Recent development in Operator Algebras
    • Place of Presentation
      (京都府京都市)京都大学数理解析研究所
    • Year and Date
      2016-09-12
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Some operator inequalities which characterize operator means2016

    • Author(s)
      H. Osaka
    • Organizer
      ILAS2016
    • Place of Presentation
      (ベルギー)ルーベン
    • Year and Date
      2016-07-15
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Tracial approximation for inclusions of unital C*-algebras2016

    • Author(s)
      H. Osaka
    • Organizer
      International conference on structure of C*-algebras and tracial approximation
    • Place of Presentation
      (中国)Shijiazhuang
    • Year and Date
      2016-07-07
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Generalized reverse Cauchy inequality and applications to operator means2016

    • Author(s)
      H. Osaka
    • Organizer
      KOTAC 2016
    • Place of Presentation
      (韓国)ソウル
    • Year and Date
      2016-06-21
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The Rokhlin property for group actions on Hilbert C*-modules2016

    • Author(s)
      H. Osaka
    • Organizer
      Special week on Operator Algebras in June 2016
    • Place of Presentation
      (中国)上海
    • Year and Date
      2016-06-07
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Symmetric operator monotone functions and operator means2015

    • Author(s)
      H. Osaka
    • Organizer
      作用素論・作用素環論研究集会
    • Place of Presentation
      KKR妙高高原白樺荘(新潟県妙高市)
    • Year and Date
      2015-10-25
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Some operator inequalities which characterize operator means2015

    • Author(s)
      大坂博幸, 和田州平, 鶴見幸大
    • Organizer
      日本数学会2015年度秋期総合分科会
    • Place of Presentation
      京都産業大学(京都府京都市)
    • Year and Date
      2015-09-15
    • Related Report
      2015 Research-status Report
  • [Presentation] Some operator inequalities which characterize operator means2015

    • Author(s)
      H. Osaka
    • Organizer
      Workshop on Quantum information theory and related topics
    • Place of Presentation
      (ベトナム)ハノイ
    • Year and Date
      2015-09-01
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] The Rokhlin property for an inclusion of C*-algebras2015

    • Author(s)
      H. Osaka
    • Organizer
      Special Week on Operator Algebras
    • Place of Presentation
      (中国)上海
    • Year and Date
      2015-06-03
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Gaps problem of matrix monotone functions and matrix convex functions and their applications2015

    • Author(s)
      大坂博幸
    • Organizer
      日本数学会2015年度春期総合分科会
    • Place of Presentation
      明治大学(東京都)
    • Year and Date
      2015-03-22
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 非対称な作用素平均について2015

    • Author(s)
      大坂博幸
    • Organizer
      関数解析学の研究とその応用
    • Place of Presentation
      新潟大学(新潟県)
    • Year and Date
      2015-01-30
    • Related Report
      2014 Research-status Report
  • [Presentation] SELF-ADJOINTNESS AND SYMMETRICITY OF OPERATOR MEANS2014

    • Author(s)
      大坂博幸
    • Organizer
      作用素の平均とその関連
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Year and Date
      2014-11-28
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] The Jiang-Su absorption for inclusions of unital C*-algebras2014

    • Author(s)
      大坂博幸, 照屋保
    • Organizer
      日本数学会2014年度秋期総合分科会
    • Place of Presentation
      広島大学(広島県)
    • Year and Date
      2014-09-27
    • Related Report
      2014 Research-status Report
  • [Presentation] The Jiang-Su absorption for inclusions of unital C*-algebras2014

    • Author(s)
      H. Osaka
    • Organizer
      ICM Satillite Conference on Operator algebras and Applications
    • Place of Presentation
      (韓国)ソウル
    • Year and Date
      2014-08-09
    • Related Report
      2014 Research-status Report
  • [Remarks] 立命館大学研究者学術情報データベース

    • URL

      http://research-db.ritsumei.ac.jp/scrips/websearch/index.htm

    • Related Report
      2016 Annual Research Report
  • [Remarks] 立命館大学研究者学術データーベース

    • URL

      http://research-db.ritsumei.ac.jp/scripts/websearch/index.htm

    • Related Report
      2015 Research-status Report
  • [Remarks] 立命館大学研究者学術情報データベース

    • URL

      http://research-db.ritsumei.ac.jp/scripts/websearch/index.htm

    • Related Report
      2014 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2022-02-22  

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