Characterization of the Hilbert ball by its Automorphisms

2002/12/02 by Kang-Tae Kim, Kim, Kang-Tae, Daowei Ma +1
Mathematics · #32M05 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:32M05

paper · pdf · doi:10.48550/arxiv.math/0212023

13 pages

arxiv created 2002/12/02 · arxiv updated 2009/11/30

Abstract

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

Related

• Characterization of the Hilbert ball by its automorphism group
• Quasiconformal variants of the Wong--Rosay theorem
• A Wong-Rosay type theorem for proper holomorphic self-maps
• Local automorphisms of the Hilbert ball
• Some aspects of the Kobayashi and Carathéodory metrics on pseudoconvex domains