The Caratheodory-Cartan-Kaup-Wu Theorem on an infinite-dimensional Hilbert space
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SCOPUS
- Title
- The Caratheodory-Cartan-Kaup-Wu Theorem on an infinite-dimensional Hilbert space
- Authors
- Cima, JA; Graham, I; Kim, KT; Krantz, SG
- Date Issued
- 2007-03
- Publisher
- NAGOYA UNIV
- 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
- NORMAL-FAMILIES; HOLOMORPHIC MAPPINGS; COMPLEX
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/29500
- DOI
- 10.1017/S0027763000025721
- ISSN
- 0027-7630
- Article Type
- Article
- Citation
- NAGOYA MATHEMATICAL JOURNAL, vol. 185, page. 17 - 30, 2007-03
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