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# Subadditivity Inequalities for Compact Operators

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Published:2012-05-30
Printed: Mar 2014
• Jean-Christophe Bourin,
Laboratoire de mathématiques, Université de Franche-Comté, 25\,000 Besaçon, France
• Tetsuo Harada,
6-12-28-102 Tamura, Sawaraku, Fukuoka 814-0175, Japan
• Eun-Young Lee,
Department of mathematics, Kyungpook National University, Daegu 702-701, Korea
 Format: LaTeX MathJax PDF

## Abstract

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.
 Keywords: concave or convex function, Hilbert space, unitary orbits, compact operators, compressions, matrix inequalities
 MSC Classifications: 47A63 - Operator inequalities 15A45 - Miscellaneous inequalities involving matrices

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