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 (SANO Takash) 山形大学, 理学部, 教授 (20250912)
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| Project Period (FY) |
2008 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2008: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
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| Keywords | 関数解析 / 作用素論 / 行列解析 / 行列 / 作用素 / レウナー行列 / クオン行列 / 作用素解析 / 一般化逆 / 条件付き負 / 作用素不等式 / 作用素環論 / 作用素単調 / 作用素凸 / 条件付正 |
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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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Report
(7 results)
Research Products
(49 results)
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[Presentation] Kwong行列について2011
Author(s)
日高 知佳良、佐野隆志
Organizer
研究集会「バナッハ空間論の研究とその周辺」
Place of Presentation
京都大学数理解析研究所
Year and Date
2011-02-14
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