2017 Fiscal Year Final Research Report
Functional analytic study on infinite dimensional groups
| Project/Area Number |
26800055
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Shinshu University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 無限次元群 / ユニタリ群 / 自己共役作用素 / 同値関係 / 記述集合論 |
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| Outline of Final Research Achievements |
(1) We studied the unitary equivalence relation modulo the compacts for self-adjoint operators from a descriptive set theoretical point of view. It was shown that this equivalence relation cannot be classified by countable structures.
(2) We studied topological groups which can be embedded into the unitary group of a finite von Neumann algebra. Such groups are called finite type groups. Finite type groups admit a compatible bi-invariant metric and can be embedded into the unitary group on a Hilbert space. It was shown that these two conditions are not sufficient to be a finite type group.
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| Free Research Field |
関数解析
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