Inner ideals and facial structure of the quasi-state space of a JB-algebra
The facial structure associated with a JB-algebra \(A\) is studied in this paper. In particular, the author classifies the \(w^*\)-closed faces ontaining zero of the quasi-state space \(Q(A)\) in terms of the algebraic structure of \(A\). This study provides a new approach to the classification of the \(w^*\)-closed faces of the quasi-state space of a \(C^*\)-algebra. But unlike this special cases, due to Akemann and Pedersen, whose proof uses the Gelfand-Naimark representation, dealing with the general case of a JB-algebra requires the introduction of new techniques including the use of a new inequality of Cauchy-Schwarz type for elements of the dual of a JB-algebra.
scientific article; zbMATH DE number 1484762
scientific article