General study of operator algebras and discrete groups

• Project/Area Number: 25800065
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Osaka Kyoiku University
• Principal Investigator: Okayasu Rui 大阪教育大学, 教育学部, 准教授 (70362746)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: 作用素環 / von Neumann 環 / von Neumann algebra / Haagerup property

Outline of Final Research Achievements

I study the Haagerup approximation property for von Neumann algebras. At first, we succeed to define the Haagerup approximation property for arbitrary von Neumann algebras, and prove several expected equivalent conditions and properties.

Research Products

• [Journal Article] Haagerup approximation property via bimodules (2017)
  • Author(s): Rui Okayasu, Narutaka Ozawa, Reiji Tomatsu
  • Journal Title: Mathematica Scandinavica Volume: 印刷中
  • NAID: 120006536945
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Haagerup approximation property and positive cones associated with a von Neumann algebra (2016)
  • Author(s): Rui Okayasu, Reiji Tomatsu
  • Journal Title: the Journal of Operator Theory Volume: 75 Pages: 259-288
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Generalisations of the Haagerup approximation property to arbitrary von Neumann algebras (2014)
  • Author(s): M. Caspers, R. Okayasu, A. Skalski, R. Tomatsu
  • Journal Title: C. R. Acad. Sci. Paris Volume: 358
  • NAID: 120005460259
  • Peer Reviewed
• [Presentation] Haagerup approximation property for von Neumann algebras (2016)
  • Author(s): Rui Okayasu
  • Organizer: 実函数論・関数解析学合同シンポジウム
  • Place of Presentation: 首都大学東京
  • Year and Date: 2016-09-01
• [Presentation] Haagerup approximation property for von Neumann algebras (2016)
  • Author(s): Rui Okayasu
  • Organizer: Trimester Seminar
  • Place of Presentation: Hausdorff Research Institute for Mathematics
  • Year and Date: 2016-06-21
• [Presentation] Haagerup approximation property via bimodules (2015)
  • Author(s): Rui Okayasu
  • Organizer: The International Conference on Non-commutative Geometry and K-Theory
  • Place of Presentation: 中国・重慶
  • Year and Date: 2015-12-18
  • Int'l Joint Research / Invited
• [Presentation] Haagerup approximation property via bimodules (2015)
  • Author(s): Rui Okayasu
  • 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
  • Year and Date: 2015-10-24
  • Invited
• [Presentation] Haagerup approximation property via bimodules (2015)
  • Author(s): Rui Okayasu
  • Organizer: 日本数学会函数解析学分科会
  • Place of Presentation: 京都産業大学
  • Year and Date: 2015-09-13
• [Presentation] Haagerup approximation property for von Neumann algebras (2015)
  • Author(s): Rui Okayasu
  • Organizer: テニュアトラックミニ研究集会
  • Place of Presentation: お茶の水女子大学
  • Year and Date: 2015-03-26 – 2015-03-27
  • Invited
• [Presentation] Haagerup approximation property and positive cones associated with a von Neumann algebra (2014)
  • Author(s): Rui Okayasu
  • Organizer: 日本数学会函数解析学分科会
  • Place of Presentation: 広島大学
  • Year and Date: 2014-09-25 – 2014-09-28
• [Presentation] Haagerup approximation property and positive cones associated with a von Neumann algebra (2014)
  • Author(s): Rui Okayasu
  • Organizer: ICM Satellite Conference on Operator Algebras and Applications
  • Place of Presentation: Cheongpung, Korea
  • Year and Date: 2014-08-08 – 2014-08-14
  • Invited
• [Presentation] Haagerup approximation property and positive cones associated with a von Neumann algebra (2014)
  • Author(s): Rui Okayasu
  • Organizer: Workshop on Operator Spaces, Locally Compact Quantum Groups and Amenability
  • Place of Presentation: The Fields Institute, Canada
  • Year and Date: 2014-05-26 – 2014-05-30
  • Invited
• [Presentation] Haagerup approximation property for arbitrary von Neumann algebras
  • Author(s): 岡安類
  • Organizer: 作用素論・作用素環論研究集会
  • Place of Presentation: お茶の水女子大学
  • Invited
• [Presentation] Haagerup approximation property for arbitrary von Neumann algebras
  • Author(s): 岡安類
  • Organizer: 日本数学会函数解析学分科会
  • Place of Presentation: 学習院大学
• [Remarks] 岡安類のホームページ
  • URL: http://www.osaka-kyoiku.ac.jp/~rui/index.html
• [Remarks] Rui Okayasu
  • URL: http://www.osaka-kyoiku.ac.jp/~rui/index.html
• [Remarks] Rui OKAYASU
  • URL: http://www.osaka-kyoiku.ac.jp/~rui/index.html
• [Remarks] 岡安類
  • URL: http://www.osaka-kyoiku.ac.jp/~rui/index-j.html