Displaying similar documents to “The density condition in quotients of quasinormable Fréchet spaces, II.”

The density condition in quotients of quasinormable Fréchet spaces

Angela Albanese (1997)

Studia Mathematica

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It is proved that a separable Fréchet space is quasinormable if, and only if, every quotient space satisfies the density condition of Heinrich. This answers positively a conjecture of Bonet and Dí az in the class of separable Fréchet spaces.

The density condition and the strong dual density condition by operator.

Wolf-Dieter Heinrichs (1997)

Collectanea Mathematica

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The aim of the present article is to introduce and investigate topological properties by operator. We obtain good stability properties for the density condition and the strong dual density condition by taking injective tensor products. Further we analyze the connection to (DF)-properties by operator.

Density conditions in Fréchet and (DF)-spaces.

Klaus-Dieter. Bierstedt, José Bonet (1989)

Revista Matemática de la Universidad Complutense de Madrid

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We survey our main results on the density condition for Fréchet spaces and on the dual density condition for (DF)-spaces (cf. Bierstedt and Bonet (1988)) as well as some recent developments.

Tensor stable Fréchet and (DF)-spaces.

José Bonet, Juan Carlos Díaz, Jari Taskinen (1991)

Collectanea Mathematica

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In this paper we introduce and investigate classes of Fréchet and (DF)-spaces which constitute a very general frame in which the problem of topologies of Grothendieck and some related dual questions have a positive answer. Many examples of spaces in theses classes are provided, in particular spaces of sequences and functions. New counterexamples to the problems of Grothendieck are given.

The density condition in projective tensor products.

Wolf-Dieter Heinrichs (1999)

Revista Matemática Complutense

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In this paper we modify a construction due to J. Taskinen to get a Fréchet space F which satisfies the density condition such that the complete injective tensor product l2 x~eF'b does not satisfy the strong dual density condition of Bierstedt and Bonet. In this way a question that remained open in Heinrichs (1997) is solved.

Some aspects of the modern theory of Fréchet spaces.

Klaus D. Bierstedt, José Bonet (2003)

RACSAM

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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 duals of distinguished frechet spaces

José Bonet, Susanne Dierolf (1996)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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The purpose of this note is to give an example of a distinguished Fréchet space and a non-distinguished Fréchet space which have the same inductive dual. Accordingly, distinguishedness is a property which is not reflected in the inductive dual. In contrast to this example, it was known that the properties of being quasinormable or having the density condition can be characterized in terms of the inductive dual of a Fréchet space.