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.
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