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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
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