Biholomorphic Mappings on Banach Spaces

We present an infinite-dimensional version of Cartan's theorem concerning the existence of a holomorphic inverse of a given holomorphic self-map of a bounded convex open subset of a dual Banach space. No separability is assumed, contrary to previous analogous results. The main assumption is tha...

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Bibliographic Details
Published in:Proceedings of the Edinburgh Mathematical Society 2019-11, Vol.62 (4), p.913-924
Main Authors: Carrión, H., Galindo, P., Lourenço, M. L.
Format: Article
Language:English
Subjects:
Banach spaces
Existence theorems
Hilbert space
Mathematical analysis
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Summary:We present an infinite-dimensional version of Cartan's theorem concerning the existence of a holomorphic inverse of a given holomorphic self-map of a bounded convex open subset of a dual Banach space. No separability is assumed, contrary to previous analogous results. The main assumption is that the derivative operator is power bounded, and which we, in turn, show to be diagonalizable in some cases, like the separable Hilbert space.
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091518000883