Characterization of the extreme elements of a \(J^ *\)-algebra (Q1086470)

The author shows that each singly generated \(J^*\)-subalgebra of a \(J^*\)-algebra is \(J^*\)-isomorphic to the space \(C_ 0(X)\) of all continuous complex-valued functions vanishing at infinity on a locally compact Hausdorff space X. This result is used to extend \textit{R. V. Kadison's} classical characterization of the extreme points of the unit ball of a \(C^*\)-algebra [Ann. Math., II. Ser. 54, 325-338 (1951; Zbl 0045.062)] to the context of a \(J^*\)-algebra. As the author remarks, the result concerning singly generated \(J^*\)-subalgebras was obtained by \textit{W. Kaup} [Math. Ann. 228, 39-64 (1977; Zbl 0344.58006)], whilst the proof of the latter result generalizes the proof given by Kadison in the \(C^*\)-algebra case.