The Caratheodory-Cartan-Kaup-Wu theorem on an infinite dimensional Hilbert space

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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.

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Complex Variables, 32M99, 46C05

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http://salesiana.dossiersoluciones.com/handle/123456789/124366

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0702620
 http://arxiv.org/abs/math/0702620

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arXiv