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HOLOMORPHIC LIFTINGS FROM INFINITE DIMENSIONAL SPACES

HOLOMORPHIC LIFTINGS FROM INFINITE DIMENSIONAL SPACES We obtain a number of positive solutions to the following problem: if Ω is a domain in a locally convex space E, X and Y are Banach spaces with Y ⊂ X and quotient mapping π : X → X / Y , and ƒ : Ω → X / Y is holomorphic, does there exist a holomorphic mapping h : Ω → X such that ƒ = π º h ? The mapping h is called a (holomorphic) lifting. For example, we obtain a positive result when Ω is pseudoconvex, E is a Banach space with an unconditional basis and Y is an M -ideal in X . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematical Proceedings of the Royal Irish Academy Royal Irish Academy

HOLOMORPHIC LIFTINGS FROM INFINITE DIMENSIONAL SPACES

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References (28)

Publisher
Royal Irish Academy
Copyright
Copyright © 2011 RIA
ISSN
1393-7197
eISSN
2009-0021
DOI
10.3318/PRIA.2011.111.1.7
Publisher site
See Article on Publisher Site

Abstract

We obtain a number of positive solutions to the following problem: if Ω is a domain in a locally convex space E, X and Y are Banach spaces with Y ⊂ X and quotient mapping π : X → X / Y , and ƒ : Ω → X / Y is holomorphic, does there exist a holomorphic mapping h : Ω → X such that ƒ = π º h ? The mapping h is called a (holomorphic) lifting. For example, we obtain a positive result when Ω is pseudoconvex, E is a Banach space with an unconditional basis and Y is an M -ideal in X .

Journal

Mathematical Proceedings of the Royal Irish AcademyRoyal Irish Academy

Published: Jan 1, 2011

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