2012 Fiscal Year Final Research Report
On many approaches of the invariantsubspace problem in Hilbert spaces
| Project/Area Number |
22540184
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Shizuoka University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
SAITO Kichi-suke 新潟大学, 自然科学系, 教授 (30018949)
WATATANI Yasuo 九州大学, 数理(科)学研究科(研究院), 教授 (00175077)
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| Project Period (FY) |
2010 – 2012
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| Keywords | invariant subspace(不変部分空間) / Hilbert spaces(ヒルベルト空間) / analytic crossed products(解析的接合積) |
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| Research Abstract |
The invariant subspace problem is the question that every bounded operator on a separable Hilbert space has a non-trivial invariant subspace. There has been a large amount of work on invariant subspaces, motivated by interest in the structure of non-self adjoint operators on Hilbert space. Our purpose is to investigate this problem on many ways; theory of operator algebras, Banach spaces and Hilbert spaces. And we succeeded in development of much theory relevant to the problem.
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