The Composition Operation on Spaces of Holomorphic Mappings
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Publication:5114492
DOI10.1093/QMATHJ/HAZ035zbMATH Open1460.46026arXiv1811.08463OpenAlexW2900988162MaRDI QIDQ5114492
Pablo Galindo, Maria D. Acosta, Luiza A. Moraes
Publication date: 24 June 2020
Published in: The Quarterly Journal of Mathematics (Search for Journal in Brave)
Abstract: We discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fr'{e}chet space of the entire mappings that are bounded on bounded sets the composition turns to be even holomorphic. In such 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.
Full work available at URL: https://arxiv.org/abs/1811.08463
Infinite-dimensional holomorphy (46G20) Linear composition operators (47B33) Spaces of differentiable or holomorphic functions on infinite-dimensional spaces (46E50)
Related Items (4)
Composition operators on holomorphic variable exponent spaces ⋮ Holomorphic mappings of domains in operator spaces ⋮ The iterates of composition operators on Banach spaces of holomorphic functions ⋮ Title not available (Why is that?)
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