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The Approximation Property for Nuclear Convergence Vector Spaces

✍ Scribed by Sten Bjon

Publisher: John Wiley and Sons
Year: 1989
Tongue: English
Weight: 527 KB
Volume: 142
Category: Article
ISSN: 0025-584X
DOI: 10.1002/mana.19891420118

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✦ Synopsis

Nuclear convergence spaces are studied. I t is s h o r n that an L,-embedded convergence vector space B is L,LM-embeddsd if it is SCHWARTZ and satisfien a certain countability condition which expresses that the set of filters converging to zero is essentially countable Further it is shown that if B is L,LJpembedded and nuclear, then the identity E -E can be approximated with finite operators in the equable continuous convergence structure on L(E, E). This resiilt is used in the study of the spectrum Hom,H,( U ) of the convergence algebra He( U ) of holomorphic functions on u circled convex optw set. to prove sufficient conditions for the validity of the formula HowA,H,( U) G L/.

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