Benslimane, M.; Fernández López, Antonio; Kaī, A. Caractérisation des algèbres de Jordan-Banach de capacité finie. (Characterization of Jordan Banach algebras of finite capacity). (French) Zbl 0679.46035 Bull. Sci. Math., II. Sér. 112, No. 4, 473-480 (1988). The authors give several equivalent conditions on a semi-simple unital non commutative Jordan Banach algebra A (real or complex) which are necessary and sufficient for A to be of finite capacity, i.e. \(\mathbf{1}=e_ 1+...+e_ n\), where \(e_ i\), \(i=1,...,n\), are orthogonal completely primitive idempotents. Reviewer: Sh.Ayupov MSC: 46H70 Nonassociative topological algebras 46L05 General theory of \(C^*\)-algebras 17C50 Jordan structures associated with other structures 17D99 Other nonassociative rings and algebras Keywords:semi-simple unital non commutative Jordan Banach algebra; finite capacity; orthogonal completely primitive idempotents PDFBibTeX XMLCite \textit{M. Benslimane} et al., Bull. Sci. Math., II. Sér. 112, No. 4, 473--480 (1988; Zbl 0679.46035)