On a class of Hilbert C*-manifolds

Abstract

This paper deals with a special class of ‘non-compact’ hermitian infinite dimensional symmetric spaces, generically denoted by U. We calculate their invariant connection very explicitly and use the concept of a Hilbert C*-manifold so that the Banach manifold in question is of the form Aut U/H, where Aut U is the automorphism group of the Hilbert C*-manifold. We finally use results previously obtained with D. Blecher to characterize causal structure on U that comes from interpreting the elements of U as bounded Hilbert space operators.