2012 Fiscal Year Final Research Report
Analysis on geometric structures of operators in definite or indefinite inner product spaces
| Project/Area Number |
20540152
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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 | Yamagata University |
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Principal Investigator |
SANO Takashi 山形大学, 理学部, 教授 (20250912)
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| Project Period (FY) |
2008 – 2012
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| Keywords | 関数解析 / 作用素論 / 行列解析 |
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| Research Abstract |
For selfadjoint operators/Hermitian matrices, we can define the order structure. For a real-valued function f we know the functional calculus by f. If this operation preserves the preceding order, then we say that f is operator/matrix monotone. It is well-known that this is equivalent to the positive-semidefiniteness of the corresponding Loewner matrices to f. Rajendra Bhatia and I studied the conditional positive/negative definiteness of Loewner matrices to have their characterization with applications. Fumio Hiai and I gave more precise arguments to have their generalizations.
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