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Topological tensor products of a Fréchet-Schwartz space and a Banach space

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Peris A.

Studia Mathematica

1993

tom 106

nr 2

189-196

We exhibit examples of countable injective inductive limits E of Banach spaces with compact linking maps (i.e. (DFS)-spaces) such that $E ⊗_{ε} X$ 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 $F ⨶_π X$. 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.

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1 Studia Mathematica

1 Peris A.

1 1993

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Topological tensor products of a Fréchet-Schwartz space and a Banach space