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Projective Tensor Products of Distinguished Fréchet Spaces

✍ Scribed by José Bonet and Andreas Defant

Book ID
125203685
Year
1985
Weight
591 KB
Volume
85A
Category
Article
ISSN
0035-8975

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## Abstract Bierstedt and Bonet proved in 1988 that if a metrizable locally convex space __E__ satisfies the Heinrich's density condition, then every bounded set in the strong dual (__E__ ′, __β__ (__E__ ′, __E__)) of __E__ is metrizable; consequently __E__ is distinguished, i.e. (__E__ ′, __β__ (_

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An example of two distinguished M c h e t spaces E, F is given (even more, E is quasinormable and F is normable) such that their completed injective tensor product E&F is not distinguished. On the other hand, it is proved that for arbitrary reflexive F r k h e t space E and arbitrary compact set K t