A splitting theory for the space of distributions

P. Domański; D. Vogt

Displaying similar documents to “A splitting theory for the space of distributions”

On exact sequences of quojections.

G. Metafune, V. B. Moscatelli (1991)

Revista Matemática de la Universidad Complutense de Madrid

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We give some general exact sequences for quojections from which many interesting representation results for standard twisted quojections can be deduced. Then the methods are also generalized to the case of nuclear Fréchet spaces.

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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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. ...

The space of real-analytic functions has no basis

Paweł Domański, Dietmar Vogt (2000)

Studia Mathematica

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Let Ω be an open connected subset of $ℝ^{d}$ . We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.

Banach spaces, à la recherche du temps perdu.

Jesús M. Fernández Castillo (2000)

Extracta Mathematicae

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What follows is the opening conference of the late night seminar at the III Conference on Banach Spaces held at Jarandilla de la Vera, Cáceres. Maybe the reader should not take everything what follows too seriously: after all, it was designed for a friendly seminar, late in the night, talking about things around a table shared by whisky, preprints and almonds. Maybe the reader should not completely discard it. Be as it may, it seems to me by now that everything arrives in the nick of...

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

Susanne Dierolf (1993)

Collectanea Mathematica

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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...

Fréchet spaces of Moscatelli type.

José Bonet, Susanne Dierolf (1989)

Revista Matemática de la Universidad Complutense de Madrid

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Each Schwartz Fréchet space is a subspace of a Schwartz Fréchet space with an unconditional basis

Steven F. Bellenot (1980)

Compositio Mathematica

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