Subadditivity Inequalities for Compact Operators

Canadian mathematical bulletin

Eun-Young Lee¹  Tetsuo Harada²  Jean-Christophe Bourin³ 

[1] Department of mathematics, Kyungpook National University, Daegu 702-701, Korea;6-12-28-102 Tamura, Sawaraku, Fukuoka 814-0175, Japan;Laboratoire de mathématiques, Université de Franche-Comté, 25,000 Besaçon, France

关键词: concave or convex function;    Hilbert space;    unitary orbits;    compact operators;    compressions;    matrix inequalities;   

DOI  :  10.4153/CMB-2012-009-9

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Some subadditivity inequalities for matrices and concave functions also hold for Hilbert space operators, but (unfortunately!) with an additional $varepsilon$ term. It seems not possible to erase this residual term. However, in case of compact operators we show that the $varepsilon$ term is unnecessary. Further, these inequalities are strict in a certain sense when some natural assumptions are satisfied. The discussion also stresses on matrices and their compressions and several open questions or conjectures are considered, both in the matrix and operator settings.

【 授权许可】

Unknown