A matrix subadditivity inequality for symmetric norms

TL;DR

This paper extends subadditivity inequalities from positive operators to Hermitian and normal operators, with applications to matrix decompositions and block-matrices, broadening the scope of operator inequalities.

Contribution

It introduces a matrix subadditivity inequality for symmetric norms applicable to Hermitian and normal operators, expanding existing results for positive operators.

Findings

Extended subadditivity inequalities to Hermitian and normal operators

Applied inequalities to Cartesian decomposition and block-matrices

Broadened understanding of operator inequalities in matrix analysis

Abstract

Well-known subadditivity results for positive operators (of Brown-Kosaki and Rotfeld/Ando-Zhan types) are extended to Hermitian and normal ones. Applications to Cartesian decomposition and block-matrices are given.