Extension and splitting theorems for Fréchet spaces of type 2.

A. Defant; P. Domanski; M. Mastylo

Displaying similar documents to “Extension and splitting theorems for Fréchet spaces of type 2.”

Mittag-Leffler methods in analysis.

Jorge Mújica (1995)

Revista Matemática de la Universidad Complutense de Madrid

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In this survey we present two Mittag-Leffler lemmas and several applications to topics as varied as the delta-equation, Fréchet algebras, inductive limits of Banach spaces and quasi-normable Fréchet spaces.

Fréchet spaces of Moscatelli type.

José Bonet, Susanne Dierolf (1989)

Revista Matemática de la Universidad Complutense de Madrid

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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?. ...

On a type of linear differential equations in Fréchet spaces

George N. Galanis (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Quasinormable X-Kothe Echelon spaces.

FERNANDO BLASCO (2000)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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Standard exact projective resolutions relative to a countable class of Fréchet spaces

P. Domański, J. Krone, D. Vogt (1997)

Studia Mathematica

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We will show that for each sequence of quasinormable Fréchet spaces ${(E_{n})}_{ℕ}$ there is a Köthe space λ such that $E x t^{1} (λ (A), λ (A) = E x t^{1} (λ (A), E_{n}) = 0$ and there are exact sequences of the form $. . . \to λ (A) \to λ (A) \to λ (A) \to λ (A) \to E_{n} \to 0$ . If, for a fixed ℕ, $E_{n}$ is nuclear or a Köthe sequence space, the resolution above may be reduced to a short exact sequence of the form $0 \to λ (A) \to λ (A) \to E_{n} \to 0$ . The result has some applications in the theory of the functor $E x t^{1}$ in various categories of Fréchet spaces by providing a substitute for non-existing projective resolutions.

On the functors Ext¹(E,F) for Fréchet spaces

Dietmar Vogt (1987)

Studia Mathematica

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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.

Solution to a question of Grothendieck.

Jesús M. Fernández Castillo, Joaquín Motos (1992)

Extracta Mathematicae

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This note is to bring attention to one of the ending questions in Grothendieck's thesis [3, Chapter 2, p. 134]: Is the space D_L^p isomorphic to s ⊗ L^p? The problem has been, as we shall see, essentially solved by Valdivia and Vogt. This fact, however, seems to have remained unnoticed. Supports this belief of the authors the fact that they have been unable to find an explicit reference to its solution. ...