The Krein-Milman theorem in operator convexity

Webster, Corran; Winkler, Soren

doi:10.1090/S0002-9947-99-02364-8

The Krein-Milman theorem in operator convexity
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by Corran Webster and Soren Winkler

Trans. Amer. Math. Soc. 351 (1999), 307-322

DOI: https://doi.org/10.1090/S0002-9947-99-02364-8

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Abstract:

We generalize the Krein-Milman theorem to the setting of matrix convex sets of Effros-Winkler, extending the work of Farenick-Morenz on compact C$^*$-convex sets of complex matrices and the matrix state spaces of C$^*$-algebras. An essential ingredient is to prove the non-commutative analogue of the fact that a compact convex set $K$ may be thought of as the state space of the space of continuous affine functions on $K$.

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