Characterization of the Hilbert ball by its Automorphisms

Details Characterization of the Hilbert ball by its Automorphisms Characterization of the Hilbert ball by its Automorphisms

2002-12-02

arxiv.org/abs/math/0212023v1

Mathematics

Complex Variables

13 pages

Scientific paper

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.

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