Department of Mathematics, University of California, Los Angeles, California 90095 ; University of Wales, Swansea, Singleton Park, Swansea SA2 8PP, UK
Abstract:
We generalize the Krein-Milman theorem to the setting of matrix convex sets of Effros-Winkler, extending the work of Farenick-Morenz on compact C-convex sets of complex matrices and the matrix state spaces of C-algebras. An essential ingredient is to prove the non-commutative analogue of the fact that a compact convex set may be thought of as the state space of the space of continuous affine functions on .