Topological tensor products of a Fréchet-Schwartz space and a Banach space
Peris, Alfredo
Studia Mathematica, Tome 104 (1993), p. 189-196 / Harvested from The Polish Digital Mathematics Library
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We exhibit examples of countable injective inductive limits E of Banach spaces with compact linking maps (i.e. (DFS)-spaces) such that E⊗εX is not an inductive limit of normed spaces for some Banach space X. This solves in the negative open questions of Bierstedt, Meise and Hollstein. As a consequence we obtain Fréchet-Schwartz spaces F and Banach spaces X such that the problem of topologies of Grothendieck has a negative answer for F⨶πX. This solves in the negative a question of Taskinen. We also give examples of Fréchet-Schwartz spaces and (DFS)-spaces without the compact approximation property and with the compact approximation property but without the approximation property.

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:216012 
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     year = {1993},
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Peris, Alfredo. Topological tensor products of a Fréchet-Schwartz space and a Banach space. Studia Mathematica, Tome 104 (1993) pp. 189-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv106i2p189bwm/

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