Holomorphic functions on nuclear spaces

Boland, Philip J.

doi:10.1090/S0002-9947-1975-0388094-3

Holomorphic functions on nuclear spaces
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by Philip J. Boland

Trans. Amer. Math. Soc. 209 (1975), 275-281

DOI: https://doi.org/10.1090/S0002-9947-1975-0388094-3

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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.

References

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