On unitary convex decompositions of vectors in a JB\(^*\)-algebra. (English) Zbl 1299.46077

In this paper, decompositions of vectors as convex combinations of unitaries are studied. Based on his previous results, the author analyses asymmetric decompositions of vectors in a unital JB\(^*\)-algebra. It is well-known that JB\(^*\)-algebras form a special class of Banach Jordan algebras which contains all \(C^*\)-algebras. Some results known for \(C^*\)-algebras are generalized to the case of JB\(^*\)-algebras.


46L70 Nonassociative selfadjoint operator algebras
46H70 Nonassociative topological algebras
17C65 Jordan structures on Banach spaces and algebras
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