English

Unitary orbits of Hermitian operators with convex or concave functions

Functional Analysis 2014-02-26 v1

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.

Keywords

Cite

@article{arxiv.1109.2384,
  title  = {Unitary orbits of Hermitian operators with convex or concave functions},
  author = {Jean-Christophe Bourin and Eun-Young Lee},
  journal= {arXiv preprint arXiv:1109.2384},
  year   = {2014}
}