| Project/Area Number |
17K05278
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Osaka Kyoiku University |
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Principal Investigator |
Okayasu Rui 大阪教育大学, 教育学部, 准教授 (70362746)
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| Co-Investigator(Kenkyū-buntansha) |
縄田 紀夫 大阪大学, 大学院情報科学研究科, 准教授 (90614040)
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| Project Period (FY) |
2017-04-01 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2023)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | von Neumann環 / 因子環 / von Neumann 環 / C*-環 / 自己同型写像 / 作用素環 |
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| Outline of Final Research Achievements |
We studied injectivity and Haagerup approximation, which are approximation propertoes in operator algebras. The Haagerup approximation property was not defined for type III von Neumann algebras for many years, but through joint work with Tomatsu, it was generalized. Moreover, in joint work with Ozawa and Tomatsu, some problems in the Haagerup approximation property of quantum groups were also resolved.
We also gave an alternative proof that an injective factor on a Hilbert space with trivial bicentralizer is ITPFI.
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| Academic Significance and Societal Importance of the Research Achievements |
von Neumann 環のHaagerup近似性は有限型の場合は以前から導入されたにも関わらず、一般の場合には全くの手付かずであった。しかし近年の研究によりその重要性が改めて認識されるようになり、一般的な定義の導入が期待されていた。そこで戸松氏との共同研究により、当初の予想された困難さを回避して、簡潔な定義の導入に成功した。
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