The Composition Operation on Spaces of Holomorphic Mappings

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 s...

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Bibliographic Details
Published in:Quarterly journal of mathematics 2020-06, Vol.71 (2), p.557-572
Main Authors: Acosta, María D, Galindo, Pablo, Moraes, Luiza A
Format: Article
Language:English
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Summary: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.
ISSN:0033-5606
1464-3847
DOI:10.1093/qmathj/haz035