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The Krein-Milman theorem in operator convexity


Authors: Corran Webster and Soren Winkler
Journal: Trans. Amer. Math. Soc. 351 (1999), 307-322
MSC (1991): Primary 47D20; Secondary 46A55, 46L89
DOI: https://doi.org/10.1090/S0002-9947-99-02364-8
MathSciNet review: 1615970
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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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Additional Information

Corran Webster
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095
Address at time of publication: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: Corran.Webster@math.tamu.edu

Soren Winkler
Affiliation: University of Wales, Swansea, Singleton Park, Swansea SA2 8PP, UK
Email: SWI@simcorp.dk

DOI: https://doi.org/10.1090/S0002-9947-99-02364-8
Keywords: Krein-Milman, non-commutative convexity
Received by editor(s): January 22, 1997
Additional Notes: The first author was supported by the NSF and the second author by the EPSRC and the EU
Article copyright: © Copyright 1999 American Mathematical Society

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