CHARACTERIZATION OF THE HILBERT BALL BY ITS AUTOMORPHISMS

Title & Authors
CHARACTERIZATION OF THE HILBERT BALL BY ITS AUTOMORPHISMS
Kim, Kang-Tae; Ma, Daowei;

Abstract
We show in this paper that every domain in a separable Hilbert space, say H, which has a $\small{C^2}$ 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.
Keywords
automorphism group;Hilbert ball;weak-strong normal family;
Language
English
Cited by
1.
A note on Kim–Ma characterization of the Hilbert ball, Journal of Mathematical Analysis and Applications, 2005, 309, 2, 761
2.
Model domains in ℂ3with abelian automorphism group, Complex Variables and Elliptic Equations, 2014, 59, 3, 369
3.
Some Aspects of the Kobayashi and Carathéodory Metrics on Pseudoconvex Domains, Journal of Geometric Analysis, 2012, 22, 2, 491
4.
Characterization of the unit ball in C n among complex manifolds of dimensionn, Journal of Geometric Analysis, 2004, 14, 4, 697
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