| Project/Area Number |
10640183
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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 | 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) |
1998 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2000: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1999: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1998: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | matrix inequality / norm inequality / trace / eigenvalue inequality / operator monotone function / 凸集合 / 端点 / 同時縮小化可能性 / 束構造 |
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| Research Abstract |
We set the following three actual research objectives :
(1) study of the lattice structure of the cone of positive semi-definite operators,
(2) study of super- and lower-subadditivity related to operator concave/convex functions,
(3) study of convexity properties related to the trace.
Concerning the first objective, we have succeeded in determining the condition for a pair of operators to admit the infimum in the cone of positive semi-definite operators [Reference 2].
Concerning the second objective, we have succeeded in establishing the following inequality
|||f (A+B)|||【less than or equal】 |||f (A)+f (B)|||,
which is valid for any non-negative operator concave function f (t) on the half-line [0, ∞), any pair of positive semi-definite operators A,B and any unitarily invariant norm |||・|||
[Reference 3].
Concerning the third objective, we have obtained various estimates of the traces of multiple products of two matrices [Refernece 5]. Also we have succeeded in generalizing some known determinant and trace inequalities to majorization type inequalities for eigenvalues [Reference 7].
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