Nonunital Operator Systems and Noncommutative Convexity

Abstract We establish the dual equivalence of category generalized (i.e., potentially nonunital) operator systems and pointed compact noncommutative (nc) convex sets, extending a result Davidson 1st author. then apply this to number results about systems, some which are new even in unital setting. For example, we show that maximal minimal C*-covers system can be realized terms theC*-algebra continuous nc functions on its quasistate space, clarifying recent Connes van Suijlekom. also characterize “C*-simple” is, with simple C*-cover, their spaces. develop theory quotients extends systems. In addition, extend author Shamovich relating Choquet simplices. is C*-algebra if only space an Bauer simplex zero as extreme point, second countable locally group has Kazhdan’s property (T) for every action C*-algebra, set invariant quasistates C*-algebra.