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Published October 2018 | Submitted
Journal Article Open

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.

Additional Information

© 2018 Springer Nature Switzerland AG. Received: October 16, 2017; Revised: June 16, 2018; First Online: 18 July 2018. The author was partially supported by the NSF Grant DMS-1600186.

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August 22, 2023
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October 18, 2023