The Caratheodory-Cartan-Kaup-Wu theorem on an infinite dimensional Hilbert space
Complex Variables
2007-05-23 v1
Abstract
This paper treats a holomorphic self-mapping f: Omega --> Omega of a bounded domain Omega in a separable Hilbert space H with a fixed point p. In case the domain is convex, we prove an infinite-dimensional version of the Cartan-Caratheodory-Kaup-Wu Theorem. This is basically a rigidity result in the vein of the uniqueness part of the classical Schwarz lemma. The main technique, inspired by an old idea of H. Cartan, is iteration of the mapping f and its derivative. A normality result for holomorphic mappings in the compact-weak-open topology, due to Kim and Krantz, is used.
Keywords
Cite
@article{arxiv.math/0702620,
title = {The Caratheodory-Cartan-Kaup-Wu theorem on an infinite dimensional Hilbert space},
author = {Joseph Cima and Ian Graham and Kang-Tae Kim and Steven G. Krantz},
journal= {arXiv preprint arXiv:math/0702620},
year = {2007}
}