The Carathéodory-Cartan-Kaup-Wu theorem on an infinite-dimensional Hilbert space
نویسندگان
چکیده
This paper treats a holomorphic self-mapping f : Ω → Ω of a bounded domain Ω in a separable Hilbert space H with a fixed point p. In case the domain is convex, we prove an infinitedimensional version of the Cartan-Carathéodory-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. AMS Subject Classification: Primary 32H02, 46G20
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