J. Korean Math. Soc. 2003; 40(3): 503-516
Printed May 1, 2003
Copyright © The Korean Mathematical Society.
Kang-Tae Kim and Daowei Ma
Pohang University and Wichita State University
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
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