English

Characterization of the Hilbert ball by its Automorphisms

Complex Variables 2007-05-23 v1

Abstract

We show in this paper that every domain in a separable Hilbert space, say \cH\cH, which has a C2C^2 smooth strongly pseudoconvex boundary point at which an automorphism orbit accumulates is biholomorphic to the unit ball of \cH\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.

Keywords

Cite

@article{arxiv.math/0212023,
  title  = {Characterization of the Hilbert ball by its Automorphisms},
  author = {Kang-Tae Kim and Daowei Ma},
  journal= {arXiv preprint arXiv:math/0212023},
  year   = {2007}
}

Comments

13 pages

R2 v1 2026-07-22T16:49:56.276Z