Asymmetric decompositions of vectors in \(JB^*\)-algebras. (English) Zbl 1164.46342

The author continues his investigations of \(JB^*\)-algebras. In this article, the author establishes \(JB^*\)-algebra analogues of corresponding results on asymmetric decompositions of elements in \(C^*\)-algebras due to R. V. Kadison and G. K. Pedersen. These include the extent to which variations in the coefficients of a convex combination of unitaries in a unital \(JB^*\)-algebra permit that combination to be expressed as a convex combination of fewer unitaries in the same algebra. In the sequel, the author presents a characterization of such \(JB^*\)-algebras that are the norm closure of the set of their invertible elements, also known as \(JB^*\)-algebras of topological stable rank equal to 1.
Reviewer: Jan Paseka (Brno)


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