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Displaying similar documents to “Quasinormable spaces and the problem of topologies of Grothendieck.”

Some Grothendieck's problems in the context of the α-tensor products.

Juan A. López Molina, María José Rivera Ortún (1990)

Extracta Mathematicae

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The positive and negative results related to the problem of topologies of Grothendieck [2] have given many information on the projective and injective tensor products of Fréchet and DF-spaces. The purpose of this paper is to give some results about analogous questions in αpq-Lapresté's tensor products [4, chapitre 1] and in spaces of dominated operators Pietsch [5] for a class of Fréchet spaces having a certain kind of decomposition studied dy Bonet and Díaz [1] called...

Copies of l in tensor products.

Fernando Blasco (2000)

Extracta Mathematicae

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The problem of finding complemented copies of l in another space is a classical problem in Functional Analysis and has been studied from different points of view in the literature. Here we pay attention to complementation of l in an n-fold tensor product of l spaces because we were lead to that result in the study of Grothendieck's Problème des topologies as we shall comment later.

The symmetric tensor product of a direct sum of locally convex spaces

José Ansemil, Klaus Floret (1998)

Studia Mathematica

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An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology τ such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for ⨂ τ , s n ( F 1 ⨁ F 2 ) gives a direct proof of a recent result of Díaz and Dineen (and generalizes it to other topologies τ) that the n-fold projective symmetric and the n-fold projective “full” tensor product of a locally convex space E are isomorphic if E is isomorphic to...

Complementation in spaces of symmetric tensor products and polynomials.

Fernando Blasco (1996)

Extracta Mathematicae

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Our aim here is to announce some properties of complementation for spaces of symmetric tensor products and homogeneous continuous polynomials on a locally convex space E that have, in particular, consequences in the study of the property (BB)n,s recently introduced by Dineen [8].