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 Unitary orbits of Hermitian operators with convex or concave functions


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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.



Author: Jean-Christophe Bourin; Eun-Young Lee

Source: https://archive.org/







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