Characterization of the Hilbert ball by its Automorphisms
Abstract
We show in this paper that every domain in a separable Hilbert space, say , which has a C2 smooth strongly pseudoconvex boundary point at which an automorphism orbit accumulates is biholomorphic to the unit ball of . 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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