Barycentric decompositions in the space of weak expectations

Abstract

The space of weak expectations for a given representation of a (unital) separable C*-algebra is a compact convex set of (unital) completely positive maps in the BW topology, when it is non-empty. An application of the classical Choquet theory gives a barycentric decomposition of a weak expectation in that set. However, to complete the barycentric picture, one needs to know the extreme points of the compact convex set in question. In this article, we explicitly identify the set of extreme points of the space of weak expectations for a given representation, using operator theoretic techniques.

15p, revised the presentation, no change in the main result

Cited by in corpus (2)

• Ergodic decomposition in the space of unital completely positive maps
• Decomposable Weak Expectations