Joint Majorization in Continuous Matrix Algebras

TL;DR

This paper explores different types of joint majorization in continuous matrix algebras, establishing their relative strengths and characterizing convex hulls of joint unitary orbits, with extensions to subhomogeneous C*-algebras.

Contribution

It provides a comprehensive analysis of joint majorization notions and characterizations of convex hulls in continuous matrix algebras, extending some results to subhomogeneous C*-algebras.

Findings

Established relative strengths of joint majorization notions.

Characterized closed convex hulls of joint unitary orbits.

Extended characterizations to subhomogeneous C*-algebras.

Abstract

Various notions of joint majorization are examined in continuous matrix algebras. The relative strengths of these notions are established via proofs and examples. In addition, the closed convex hulls of joint unitary orbits are completely characterized in continuous matrix algebras via notions of joint majorization. Some of these characterizations are extended to subhomogeneous C$^*$-algebras.