Royden's lemma in infinite dimensions and Hilbert-Hartogs manifolds

Details Royden's lemma in infinite dimensions and Hilbert-Hartogs manifolds Royden's lemma in infinite dimensions and Hilbert-Hartogs manifolds

2011-12-12

arxiv.org/abs/1112.2504v1

Mathematics

Complex Variables

Scientific paper

We prove the Royden's Lemma for complex Hilbert manifolds, i.e., that a holomorphic imbedding of the closure of a finite dimensional, strictly pseudoconvex domain into a complex Hilbert manifold extends to a biholomorphic mapping onto a product of this domain with the unit ball in Hilbert space. This reduces several problems concerning complex Hilbert manifolds to open subsets of a Hilbert space. As an illustration we prove some results on generalized loop spaces of complex manifolds.

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