Maps with the Unique Extension Property and C*-Extreme Points

摘要

We investigate boundary representations in the context where Hilbert spaces are replaced by C*-modules over abelian von Neumann algebras and apply this to study C*-extreme points. We present an (unexpected) example of a weak* compact B-convex subset of B(H) without B-extreme points, where B is an abelian von Neumann algebra on a Hilbert space H. On the other hand, if A is a von Neumann algebra with a separable predual and whose finite part is injective, we show that each weak* compact A-convex subset of l(infinity) (A) is generated by its A-extreme points.