  Let $\Omega$ be a bounded, convex domain in a separable Hilbert space. The
authors prove a version of the theorem of Bun Wong, which asserts that if such
a domain admits an automorphism orbit accumulating at a strongly pseudoconvex
boundary point then it is biholomorphic to the ball. Key ingredients in the
proof are a new localization argument using holomorphic peaking functions and
the use of new ``normal families'' arguments in the construction of the limit
biholomorphism.
