An Intrinsic Order-Theoretic Characterization of the Weak Expectation Property

Abstract

We prove the following characterization of the weak expectation property for operator systems in terms of Wittstock's matricial Riesz separation property: an operator system S satisfies the weak expectation property if and only if Mq (S) satisfies the matricial Riesz separation property for every q ∈ N. This can be seen as the noncommutative analog of the characterization of simplex spaces among function systems in terms of the classical Riesz separation property.