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The Schwartz property and nuclearity of spaces of smooth and holomorphic functions in infinite dimensions

Published online by Cambridge University Press:  24 October 2008

Sten Bjon
Sten Bjon
Affiliation:
Department of Mathematics, Åbo Akademi, SF-20500 Åbo, Finland
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Extract

In [8] it was shown that a locally convex space E is a Schwartz space if and only if the convergence algebras Hc(U) and He(U) of holomorphic functions on an open subset of E coincide, i.e. if and only if continuous convergence c (see [1]) and the associated equable convergence structure e (= local uniform convergence, see [2, 13]) coincide.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 107 , Issue 2 , March 1990 , pp. 377 - 385
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

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