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arXiv · 1109.2384

Unitary orbits of Hermitian operators with convex or concave functions

Jean-Christophe Bourin·Eun-Young Lee
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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 super-additivity 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.

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Jean-Christophe Bourin, Eun-Young Lee. 2011-09-12. Unitary orbits of Hermitian operators with convex or concave functions. https://doi.org/10.1112/blms%2Fbds080

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