The Composition Operation on Spaces of Holomorphic Mappings-Reference-Cited by-同舟云学术

The Composition Operation on Spaces of Holomorphic Mappings

Published:2020-02-25 Issue:2 Volume:71 Page:557-572
ISSN:0033-5606
Container-title:The Quarterly Journal of Mathematics
language:en
Short-container-title:

Author:

Acosta María D¹,Galindo Pablo²,Moraes Luiza A³

Affiliation:

1. Departamento de Análisis Matemático, Universidad de Granada, 18071 Granada, Spain

2. Departamento de Análisis Matemático, Universidad de Valencia, 46100 Valencia, Spain

3. Instituto de Matemática, Universidade Federal do Rio de Janeiro, CP 68530–CEP 21945-970, Rio de Janeiro, RJ Brazil

Abstract

Abstract We discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fréchet space of entire mappings that are bounded on bounded sets, the composition turns out to be even holomorphic. In such a space, we consider linear subspaces closed under left and right composition. We discuss the relationship of such subspaces with ideals of operators and give several examples of them. We also provide natural examples of spaces of holomorphic mappings where the composition is not continuous.

Funder

Junta de Andalucía

Spanish MINECO/FEDER

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/qjmath/article-pdf/71/2/557/33376383/haz035.pdf

Reference31 articles.

1. Oxford Graduate Texts in Mathematics;Allan,2011

2. A hereditary indecomposable $L_\infty$-space that solves the scalar-plus-compact problem;Argyros;Acta Math.,2011

3. Regularity and algebras of analytic functions in infinite dimensions;Aron;Trans. Amer. Math. Soc.,1996

4. Weakly continuous mappings on Banach spaces;Aron;J. Funct. Anal,1983

5. Compact holomorphic mappings on Banach spaces and the approximation property;Aron;J. Funct. Anal.,1976