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 M_q(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.

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