
Journal of Convex Analysis 25 (2018), No. 1, 041064 Copyright Heldermann Verlag 2018 Operator Systems and Convex Sets with Many Normal Cones Stephan Weis Departamento de Matemática, Inst. Matemática e Estatística, Univ. Estadual de Campinas, Rua S. Buarque de Holanda 651, CampinasSP / CEP 13083859, Brazil and: Centre for Quantum Information, Ecole Polytechnique, Université Libre, 50 av. F.D. Roosevelt  CP165/59, 1050 Bruxelles, Belgium maths@stephanweis.info The state space of an operator system of nbyn 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. Keywords: Normal cone, exposed ray, exposed face, coatom, operator system, state space, convex support, joint numerical range, ground state, coorbitope. MSC: 52A20, 52B05, 47L07, 51D25, 47A12; 81P16, 14P10 [ Fulltextpdf (347 KB)] for subscribers only. 