Another look at results of Wolff and Julia type for \(J^*\)-algebras (Q1916792)

Let \({\mathcal L}(H, K)\) be the space of all continuous linear operators from \(H\) to \(K\), where \(H\) and \(K\) are complex Hilbert spaces. A \(J^*\)-algebra \(U\) is a closed subspace of \({\mathcal L}(H, K)\) such that \(aa^*a\in U\) for all \(a\in U\). It was shown by Harris that the open unit ball of a \(J^*\)-algebra is a bounded symmetric domain whose transitive group of automorphisms is given by the so-called linear fractional transformations. ``In this paper, some generalizations of the classical theorem of Wolff on the unit disc in the complex field are given for \(J^*\)-algebras, using techniques from the theory of circular domains in operators spaces, as developed by \textit{L. A. Harris} [Ind. Univ. Math. J. 41, No. 1, 125-147 (1992; Zbl 0760.47018)]''.