Unitary orbits of Hermitian operators with convex or concave functions

By Jean-Christophe Bourin, Eun-Young Lee. 2011

86 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6fd706d8399151d281f37dfbcd08b4a9402eae78

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In Applied Mathematics

1. M. Sababheh
2. Hamid Reza Moradi

Citations in the corpus

• More accurate numerical radius inequalities (I) (2019, background): “It is well known that a convex function in the usual sense is not necessarily operator convex, and it is also known that the function f(t) = t, r > 0 defined on [0,∞) is operator convex if and only if r ∈ [1, 2].”