Displaying similar documents to “Localization and duality of topological tensor-products.”

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

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

Extracta Mathematicae

Similarity:

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...

Some aspects of the modern theory of Fréchet spaces.

Klaus D. Bierstedt, José Bonet (2003)

RACSAM

Similarity:

We survey some recent developments in the theory of Fréchet spaces and of their duals. Among other things, Section 4 contains new, direct proofs of properties of, and results on, Fréchet spaces with the density condition, and Section 5 gives an account of the modern theory of general Köthe echelon and co-echelon spaces. The final section is devoted to the developments in tensor products of Fréchet spaces since the negative solution of Grothendieck?s ?problème des topologies?. ...

Inductive limits of vector-valued sequence spaces.

José Bonet, Susanne Dierolf, Carmen Fernández (1989)

Publicacions Matemàtiques

Similarity:

Let L be a normal Banach sequence space such that every element in L is the limit of its sections and let E = ind E be a separated inductive limit of the locally convex spaces. Then ind L(E) is a topological subspace of L(E).

On the three-space problem and the lifting of bounded sets.

Susanne Dierolf (1993)

Collectanea Mathematica

Similarity:

We exhibit a general method to show that for several classes of Fréchet spaces the Three-space-problem fails. This method works for instance for the class of distinguished Fréchet spaces, for Fréchet spaces with the density condition and also for dual Fréchet spaces (which gives a negative answer to a question of D. Vogt). An example of a Banach space, which is not a dual Banach space but the strong dual of a DF-space, shows that there are two real different possibilities of defining...