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• W2029689519 abstract "In 2006, Arveson resolved a long-standing problem by showing that for any element $x$ of a separable self-adjoint unital subspace $Ssubseteq B(H)$, $|x|=sup|pi(x)|$, where $pi$ runs over the boundary representations for $S$. Here we show that sup can be replaced by max. This implies that the Choquet boundary for a separable operator system is a boundary in the classical sense; a similar result is obtained in terms of pure matrix states when $S$ is not assumed to be separable. For matrix convex sets associated to operator systems in matrix algebras, we apply the above results to improve the Webster-Winkler Krein-Milman theorem." @default.
• W2029689519 created "2016-06-24" @default.
• W2029689519 creator A5052129640 @default.
• W2029689519 date "2011-10-19" @default.
• W2029689519 modified "2023-09-27" @default.
• W2029689519 title "Boundary representations and pure completely positive maps" @default.
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• W2029689519 hasPublicationYear "2011" @default.
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