Study on permenent properties for inclusion of C*-algebras

• Project/Area Number: 26400125
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Ritsumeikan 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: ¥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)
• Keywords: Rokhlin 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.

Research Products

• [Int'l Joint Research] IIT Bombay/IIT Hyderabad(インド)
• [Int'l Joint Research] Indian Institute of Technology Bombay(India)
• [Int'l Joint Research] Mathematical Institute/Institute for computational Sciences(ベトナム)
• [Journal Article] Permanence of nuclear dimension for inclusions of unital C*-algebras with the Rokhlin property (2017)
  • Author(s): H. Osaka and T. Teruya
  • Journal Title: Advances in Operator Theory Volume: 印刷中
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] The generalized reverse Cauchy inequality (2016)
  • 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
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Matrix monotone functions and the generalized Powers-Stormer inequality (2016)
  • 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
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Unexpected relations which characterize operator means (2016)
  • Author(s): H. Osaka and S. Wada
  • Journal Title: Proceedings of the Amerian Mathematical Society, Series B Volume: 3 Pages: 9-17
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Inequalities for interpolation functions (2015)
  • Author(s): Dinh Trung Hoa and H. Osaka
  • Journal Title: Banach J. Math. Anal. Volume: 9 Pages: 67-74
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Interpolation classes and matrix means (2015)
  • Author(s): Dinh Trung Hoa, Toan M. Ho, and H. Osaka
  • Journal Title: Banach J. Math. Anal. Volume: 9 Pages: 140-152
  • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Characterization of operator monotone functions by Powers-Størmer type inequalities (2015)
  • Author(s): Dinh Trung Hoa, H. Osaka, and J. Tomiyama
  • Journal Title: Linear Multilinear Algebras Volume: 63 Pages: 1577-1589
  • 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 index (2014)
  • Author(s): H. Osaka and T. Teruya
  • Journal Title: Trans. Amer. Math. Soc. Volume: 366 Pages: 1685-1702
  • Peer Reviewed / Open Access
• [Presentation] Matrix functions, matrix means, matrix inequalities (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Generalized reverse Cauchy inequality and applications to operator means (2016)
  • 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
• [Presentation] The Rokhlin property for group actions on Hilbert C*-modules (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Some operator inequalities which characterize operator means (2016)
  • Author(s): H. Osaka
  • Organizer: ILAS2016
  • Place of Presentation: (ベルギー)ルーベン
  • Year and Date: 2016-07-15
  • Int'l Joint Research / Invited
• [Presentation] Tracial approximation for inclusions of unital C*-algebras (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Generalized reverse Cauchy inequality and applications to operator means (2016)
  • Author(s): H. Osaka
  • Organizer: KOTAC 2016
  • Place of Presentation: (韓国)ソウル
  • Year and Date: 2016-06-21
  • Int'l Joint Research / Invited
• [Presentation] The Rokhlin property for group actions on Hilbert C*-modules (2016)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] Symmetric operator monotone functions and operator means (2015)
  • 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
  • Invited
• [Presentation] Some operator inequalities which characterize operator means (2015)
  • 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
• [Presentation] Some operator inequalities which characterize operator means (2015)
  • 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
  • Int'l Joint Research / Invited
• [Presentation] The Rokhlin property for an inclusion of C*-algebras (2015)
  • Author(s): H. Osaka
  • Organizer: Special Week on Operator Algebras
  • Place of Presentation: (中国)上海
  • Year and Date: 2015-06-03
  • Int'l Joint Research / Invited
• [Presentation] Gaps problem of matrix monotone functions and matrix convex functions and their applications (2015)
  • 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
  • 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
• [Presentation] SELF-ADJOINTNESS AND SYMMETRICITY OF OPERATOR MEANS (2014)
  • 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
  • Invited
• [Presentation] The Jiang-Su absorption for inclusions of unital C*-algebras (2014)
  • 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
• [Presentation] The Jiang-Su absorption for inclusions of unital C*-algebras (2014)
  • 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
• [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
• [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
• [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