Weak-type normal families of holomorphic mappings in Banach spaces and characterization of the Hilbert ball by its automorphism group |
| |
Authors: | Jisoo Byun Hervé Gaussier Kang-Tae Kim |
| |
Institution: | (1) Department of Mathematics, Pohang University of Science and Technology, 790-784 Pohang, The Republic of Korea;(2) CMI Université de Provence, Marseille, France |
| |
Abstract: | We present a characterization of the open unit ball in a separable infinite dimensional Hilbert space by the property of automorphism
orbits among the domains that are not necessarily bounded. This generalizes the recent work of Kim and Krantz 6]. Key new
features of this article include: a lower bound estimate of the Kobayashi metric and distance near a pluri-subharmonic peak
boundary point of the domains in Banach spaces, an effective localization argument, and an improvement of weak-type convergence
of sequences of biholomorphic mappings of domains in Banach spaces. |
| |
Keywords: | Math Subject Classifications" target="_blank">Math Subject Classifications 32A07 |
本文献已被 SpringerLink 等数据库收录! |