spaces on bounded symmetric domains
Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball in a J*-algebra of operators. Let be the family of all collectively compact subsets W contained in . We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when is a Cartan factor.
In an earlier paper, the first two authors have shown that the convolution of a function continuous on the closure of a Cartan domain and a -invariant finite measure on that domain is again continuous on the closure, and, moreover, its restriction to any boundary face depends only on the restriction of to and is equal to the convolution, in , of the latter restriction with some measure on uniquely determined by . In this article, we give an explicit formula for in terms of ,...
Let be a bounded symmetric domain in and an irreducible arithmetic lattice which operates freely on . We prove that the cusp–compactification of is hyperbolic.