Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CHARACTERIZATION OF THE HILBERT BALL BY ITS AUTOMORPHISMS

  • Kim, Kang-Tae (Department of Mathematics Pohang University of Science and Technology) ;
  • Ma, Daowei (Department of Mathematics Wichita State University)
  • Published : 2003.05.06
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Abstract

We show in this paper that every domain in a separable Hilbert space, say H, which has a $C^2$ smooth strongly pseudoconvex boundary point at which an automorphism orbit accumulates is biholomorphic to the unit ball of 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.

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References

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