Geodesic
Operator Systems and Convex Sets with Many Normal Cones
Journal of convex analysis, Tome 25 (2018) no. 1, pp. 41-64
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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.
Classification : 52A20, 52B05, 47L07, 51D25, 47A12, 81P16, 14P10
Mots-clés : Normal cone, exposed ray, exposed face, coatom, operator system, state space, convex support, joint numerical range, ground state, coorbitope 
@article{JCA_2018_25_1_JCA_2018_25_1_a2,
     author = {S. Weis},
     title = {Operator {Systems} and {Convex} {Sets} with {Many} {Normal} {Cones}},
     journal = {Journal of convex analysis},
     pages = {41--64},
     year = {2018},
     volume = {25},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_1_JCA_2018_25_1_a2/}
}
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S. Weis. Operator Systems and Convex Sets with Many Normal Cones. Journal of convex analysis, Tome 25 (2018) no. 1, pp. 41-64. http://geodesic.mathdoc.fr/item/JCA_2018_25_1_JCA_2018_25_1_a2/