Characterization of the Hilbert ball by its automorphisms

Abstract

We show in this paper that every domain in a separable Hilbert space, say R, which has a C-2 smooth strongly pseudoconvex boundary point at which an automorphism orbit accumulates is biholomorphic to the unit ball of R. This is the complete generalization of the Wong-Rosay theorem to a separable Hilbert space of infinite dimension. Our work here is an improvement from the preceding work of Kim/Krantz [16] and subsequent improvement of Byun/Gaussier/Kim [3] in the infinite dimensions.