2013 Fiscal Year Final Research Report
Research on the relative position of subspaces of a Hilbert space and operators
| Project/Area Number |
23654053
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Basic analysis
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| Research Institution | Kyushu University |
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Principal Investigator |
WATATANI Yasuo 九州大学, 数理(科)学研究科(研究院), 教授 (00175077)
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| Co-Investigator(Renkei-kenkyūsha) |
ENOMOTO Masatoshi 甲子園大学, 総合教育研究機構 (70185130)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 関数解析 / ヒルベルト空間 / 部分空間の配置 / 直既約 / 拡大ディンキン図形 |
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| Research Abstract |
We study the relative position of n subspaces of a Hilbert space. It is important to consider indecomposable position. The case of n =1 and n =2 are solved. In finite dimensional Hilbert space, the case of n =3 and n =4 are solved and the indecomposable n subspaces are completely classified.
But infinite dimensional Hilbert space, even the case of n =3 and n =4 are still unsolved.
In our study, we attacked it by considering an analog of operator theory. We began to study Hilbert representations of quivers, which associate Hilbert spaces and operators for vertices and arrows of quivers. We investigate a complement in an infinite dimensional Hilbert space for Gabriel theorem using Dynkin diagrams A, D and E. We show that there exist infinite dimensional indecomposable Hilbert representations for extended Dynkin diagrams.
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