Krein-Milman-type problems for compact matricially convex sets (Q1183196)

The author considers matricially convex sets. These are certain linear combinations with matrix valued convex coefficients. The author shows: If \(K\) is a set of complex \(n\times n\) matrices which is compact \(\mathbb{C}^*\)-convex and generated by a compact set of normals, then \(K\) is the \(\mathbb{C}^*\)-hull of its extreme points. Let \(S\) be a set of complex \(n\times n\) matrices which is compact, hypoconvex, and which contains only normals, then the \(\mathbb{C}^*\)-hull of \(S\) possesses a \(\mathbb{C}^*\)-extreme point.