Structure spaces and decomposition in JB*-triples

Abstract

Complex Banach spaces for which the group of biholomorphic automorphisms of the open unit ball acts transitively, alias JB*-triples, possess a ternary algebraic structure uniquely determined by the holomorphic properties of the open unit ball [21]. A large and important class of these spaces is comprised of the JC*-triples of [17] (known also as J*-algebras) which are up to isometry the norm closed subspaces of B H;K†, where H and K are complex Hilbert spaces, that are closed under the ternary product