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Unitary orbits of Hermitian operators with convex or concave functions

Unitary orbits of Hermitian operators with convex or concave functions This short but self‐contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen‐, sub‐ or superadditivity‐type inequalities are considered. Some of them are substitutes to classical inequalities (Choi, Davis, Hansen–Pedersen) for operator convex or concave functions. Various trace, norm and determinantal inequalities are derived. Combined with an interesting decomposition for positive semi‐definite matrices, several results for partitioned matrices are also obtained. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Unitary orbits of Hermitian operators with convex or concave functions

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References (31)

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/bds080
Publisher site
See Article on Publisher Site

Abstract

This short but self‐contained survey presents a number of elegant matrix/operator inequalities for general convex or concave functions, obtained with a unitary orbit technique. Jensen‐, sub‐ or superadditivity‐type inequalities are considered. Some of them are substitutes to classical inequalities (Choi, Davis, Hansen–Pedersen) for operator convex or concave functions. Various trace, norm and determinantal inequalities are derived. Combined with an interesting decomposition for positive semi‐definite matrices, several results for partitioned matrices are also obtained.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Dec 1, 2012

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