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Operator systems and convex sets with many normal cones

par Weis, Stephan
Référence Journal of convex analysis, 25, 1, page (41-64)
Publication Publié, 2018

Article révisé par les pairs

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Résumé :

The state space of an operator system of n-by-n matrices has, in a sense, many normal cones. This wealth of normal cones is a smoothness quality and it implies that each exposed face is an intersection of maximal exposed faces. A clustering property of exposed faces follows. We work on minimizing the assumptions which allow an arbitrary convex set of finite dimension to have analogous properties. One motivation for this work is an isomorphism from the exposed faces of the state space to the ground state spaces of the operator system.