Siddiqui, Akhlaq A. Asymmetric decompositions of vectors in \(JB^*\)-algebras. (English) Zbl 1164.46342 Arch. Math., Brno 42, No. 2, 159-166 (2006). 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) MSC: 46H70 Nonassociative topological algebras 46L70 Nonassociative selfadjoint operator algebras 17C65 Jordan structures on Banach spaces and algebras Keywords:\(C^*\)-algebras; Jordan algebras; unitary isotopes PDFBibTeX XMLCite \textit{A. A. Siddiqui}, Arch. Math., Brno 42, No. 2, 159--166 (2006; Zbl 1164.46342) Full Text: EuDML EMIS