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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Holomorphic functions on nuclear spaces
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by Philip J. Boland PDF
Trans. Amer. Math. Soc. 209 (1975), 275-281 Request permission

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.
References
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • 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