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