The Composition Operation on Spaces of Holomorphic Mappings

6533b824fe1ef96bd12813d2

RESEARCH PRODUCT

The Composition Operation on Spaces of Holomorphic Mappings

María D. Acosta Pablo Galindo Luiza A. Moraes

subject

Pure mathematics General Mathematics 010102 general mathematics 0103 physical sciences Holomorphic function 010307 mathematical physics 0101 mathematics Composition (combinatorics)01 natural sciences Mathematics

description

AbstractWe 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.

year	journal	country	edition	language
2020-02-25	The Quarterly Journal of Mathematics

https://doi.org/10.1093/qmathj/haz035

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