Journal of the
Korean Mathematical Society JKMS

We show in this paper that every domain in a separable Hilbert space, say $\mathcal H$, which has a $C^2$ smooth strongly pseudoconvex boundary point at which an automorphism orbit accumulates is biholomorphic to the unit ball of $\mathcal H$. 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 [10] and subsequent improvement of Byun/Gaussier/Kim [3] in the infinite dimensions.

Keywords: automorphism group, Hilbert ball, weak-strong normal family

MSC numbers: Primary 32M05