OperatorTheoretic Methods for Matrix Inequalities
Project/Area Number  08640230 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  Hokusei Gakuen University 
Principal Investigator 
ANDO Tsuyoshi Hokusei Gakuen University, Faculty of Economics, Professor, 経済学部, 教授 (10001679)

CoInvestigator(Kenkyūbuntansha) 
OKUBO Kazuyoshi Hokkaido University of Education, Faculty of Education, Professor, 教育学部, 教授 (80113661)

Project Fiscal Year 
1996 – 1997

Project Status 
Completed(Fiscal Year 1997)

Budget Amount *help 
¥2,200,000 (Direct Cost : ¥2,200,000)
Fiscal Year 1997 : ¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1996 : ¥1,100,000 (Direct Cost : ¥1,100,000)

Keywords  matrix inequality / eignvalue inequality / norm inequality / Holder type inequality / Hadamard product / majorization / 行列不等式 / 固有値不等式 / ノルム不等式 / ヘルダー型不等式 / アダマル積 / マジョリゼーション / 作用素半径 / ノルム評価 / 擬順序 
Research Abstract 
1 The Goldenthompson 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 OperatorTheoretic Methods for Matrix Inequalities is prepared to let the results widely be recognized by researchers in the world. これらの成果を含め,この研究で得られた成果を広く世界の研究者に理解してもらうために,英文の報告書を作成した。

Report
(4results)
Research Output
(18results)