𝐶*-extreme points of some compact 𝐶*-convex sets

Abstract

In the C ∗ {C^{\ast }} -algebra M n {M_n} of complex n × n n \times n matrices, we consider the notion of noncommutative convexity called C ∗ {C^{\ast }} -convexity and the corresponding notion of a C ∗ {C^{\ast }} -extreme point. We prove that each irreducible element of M n {M_n} is a C ∗ {C^{\ast }} -extreme point of the C ∗ {C^{\ast }} -convex set it generates, and we classify the C ∗ {C^{\ast }} -extreme points of any C ∗ {C^{\ast }} -convex set generated by a compact set of normal matrices.