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Biholomorphic Mappings on Banach Spaces

Part of: General theory of linear operators Measures, integration, derivative, holomorphy

Published online by Cambridge University Press:  27 February 2019

H. Carrión ,
P. Galindo  and
M. L. Lourenço
H. Carrión
Affiliation:
Departamento de Matemática, Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, CEP: 05315-970, São Paulo, Brazil ([email protected]; [email protected])
P. Galindo
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia 46.100, Burjasot-Valencia, Spain ([email protected])
M. L. Lourenço
Affiliation:
Departamento de Matemática, Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, CEP: 05315-970, São Paulo, Brazil ([email protected]; [email protected])
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Abstract

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.

Keywords

automorphismbiholomorphic mappingpower-bounded operator

MSC classification

Primary: 46G20: Infinite-dimensional holomorphy 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 4 , November 2019 , pp. 913 - 924
Copyright
Copyright © Edinburgh Mathematical Society 2019 

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