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An Intrinsic Order-Theoretic Characterization of the Weak Expectation Property

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Abstract

We prove the following characterization of the weak expectation property for operator systems in terms of an approximate version of Wittstock’s matricial Riesz separation property: an operator system S satisfies the weak expectation property if and only if \(M_{q}\left( S\right) \) satisfies the approximate matricial Riesz separation property for every \(q\in \mathbb {N}\). 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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Acknowledgements

We thank the anonymous referee for their carefully reading of the manuscript, and for pointing out a mistake in the original version

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  1. Martino Lupini

    Present address: School of Mathematics and Statistics, Victoria University of Wellington, PO Box 600, Wellington, 6140, New Zealand

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  1. Mathematics Department, California Institute of Technology, 1200 E. California Blvd MC 253-37, Pasadena, CA, 91125, USA

    Martino Lupini

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  1. Martino Lupini
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Correspondence to Martino Lupini.

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The author was partially supported by the NSF Grant DMS-1600186.

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Lupini, M. An Intrinsic Order-Theoretic Characterization of the Weak Expectation Property. Integr. Equ. Oper. Theory 90, 55 (2018). https://doi.org/10.1007/s00020-018-2479-x

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