1997 Fiscal Year Final Research Report Summary
Operator-Theoretic Methods for Matrix Inequalities
| Project/Area Number |
08640230
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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 |
解析学
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| Research Institution | Hokusei Gakuen University |
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Principal Investigator |
ANDO Tsuyoshi Hokusei Gakuen University, Faculty of Economics, Professor, 経済学部, 教授 (10001679)
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| Co-Investigator(Kenkyū-buntansha) |
OKUBO Kazuyoshi Hokkaido University of Education, Faculty of Education, Professor, 教育学部, 教授 (80113661)
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| Project Period (FY) |
1996 – 1997
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| Keywords | matrix inequality / eignvalue inequality / norm inequality / Holder type inequality / Hadamard product / majorization |
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| Research Abstract |
1 The Golden-thompson inequality concerning exponential functions for a pair of matrices is generalized to the case of more than three matrices by using Hadamard products.[Reference 1]
2 Performing inverse operations before and after a positive linear map produces stronger order relation. The fundamental structure of this strong order is analyzed.[Reference 2]
3 A reasonable upper bound is given for the farthest distance from one normal matrix to the set of unitary orbits of the other normal matrix.[Reference 3]
4 Besides the usual norms, a family of operator radii omega_<rho>(・)(0<rho<*) is considered in the space of matrices. An interpolation theorem, in the form of Holder type inequality, is established for this family of operator radii with respect to Hadamard multiplication. [Reference 4, 5]
5 A way of generalizing the Holder type inequality to the matrix case is investigated. They are established in the form of matrix inequality as well as in the trace inequality. [Reference 6]
A survey article with title Operator-Theoretic Methods for Matrix Inequalities is prepared to let the results widely be recognized by researchers in the world.
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