An Intrinsic Order-Theoretic Characterization of the Weak Expectation Property

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 MqS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M_{q}\left( S\right) $$\end{document} satisfies the approximate matricial Riesz separation property for every q∈N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q\in \mathbb {N}$$\end{document}. 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.