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Transactions of the American Mathematical Society

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Holomorphic functions on nuclear spaces


Author: Philip J. Boland
Journal: Trans. Amer. Math. Soc. 209 (1975), 275-281
MSC: Primary 46G05; Secondary 46A30
DOI: https://doi.org/10.1090/S0002-9947-1975-0388094-3
MathSciNet review: 0388094
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Abstract: The space $ \mathcal{H}(E)$ of holomorphic functions on a quasi-complete nuclear space is investigated. If $ \mathcal{H}(E)$ is endowed with the compact open topology, it is shown that $ \mathcal{H}(E)$ is nuclear if and only if $ E'$ (continuous dual of $ E$) is nuclear. If $ E$ is a $ \mathcal{D}FN$ (dual of a Fréchet nuclear space) and $ F$ is a closed subspace of $ E$, then the restriction mapping $ \mathcal{H}(E) \to \mathcal{H}(F)$ is a surjective strict morphism.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0388094-3
Article copyright: © Copyright 1975 American Mathematical Society

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