Weak majorization, doubly substochastic maps, and some related inequalities in Euclidean Jordan algebras

Abstract

In this paper, we extend the notion of weak majorization and doubly substochastic maps, and the Hardy-Littlewood-Pólya theorem on majorization to Euclidean Jordan algebras. We also provide a characterization of doubly substochastic maps on Euclidean Jordan algebras in terms of Jordan algebra automorphisms and quadratic representations. In conjunction with that, various weak majorization inequalities of Aujla-Silva are generalized to Euclidean Jordan algebras.