Displaying similar documents to “ L 1 spaces fail a certain approximative property.”

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

Alfredo Peris (1993)

Studia Mathematica

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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 ⊗ 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....