Geodesic
Topological tensor products of a Fréchet-Schwartz space and a Banach space
Studia Mathematica, Tome 106 (1993) no. 2, pp. 189-196 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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. 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.
DOI : 10.4064/sm-106-2-189-196
Keywords: Fréchet-Schwartz spaces, (DFS)-spaces, topological tensor products, approximation property, compact approximation property 
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     title = {Topological tensor products of a {Fr\'echet-Schwartz} space and a {Banach} space},
     journal = {Studia Mathematica},
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Alfredo Peris. Topological tensor products of a Fréchet-Schwartz space and a Banach space. Studia Mathematica, Tome 106 (1993) no. 2, pp. 189-196. doi: 10.4064/sm-106-2-189-196

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