On exact sequences of quojections.

G. Metafune; V. B. Moscatelli

Displaying similar documents to “On exact sequences of quojections.”

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. ...

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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On non-primary Fréchet Schwartz spaces

J. Díaz (1997)

Studia Mathematica

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Let E be a Fréchet Schwartz space with a continuous norm and with a finite-dimensional decomposition, and let F be any infinite-dimensional subspace of E. It is proved that E can be written as G ⨁ H where G and H do not contain any subspace isomorphic to F. In particular, E is not primary. If the subspace F is not normable then the statement holds for other quasinormable Fréchet spaces, e.g., if E is a quasinormable and locally normable Köthe sequence space, or if E is a space of holomorphic...

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.

Fréchet spaces of continuous vector-valued functions: Complementability in dual Fréchet spaces and injectivity

P. Domański, L. Drewnowski (1992)

Studia Mathematica

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Fréchet spaces of strongly, weakly and weak*-continuous Fréchet space valued functions are considered. Complete solutions are given to the problems of their injectivity or embeddability as complemented subspaces in dual Fréchet spaces.

A splitting theory for the space of distributions

P. Domański, D. Vogt (2000)

Studia Mathematica

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The splitting problem is studied for short exact sequences consisting of countable projective limits of DFN-spaces (*) 0 → F → X → G → 0, where F or G are isomorphic to the space of distributions D'. It is proved that every sequence (*) splits for F ≃ D' iff G is a subspace of D' and that, for ultrabornological F, every sequence (*) splits for G ≃ D' iff F is a quotient of D'

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

Dietmar Vogt (1987)

Studia Mathematica

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On the three-space property: non-containment of l, 1 ≤ p < ∞, or c subspaces.

Juan Carlos Díaz Alcaide (1993)

Publicacions Matemàtiques

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The main result in this paper is the following: Let E be a Fréchet space having a normable subspace X isomorphic to l, 1 ≤ p < ∞, or to c. Let F be a closed subspace of E. Then either F or E/F has a subspace isomorphic to X.

Characterization of subspaces and quotients of nuclear $L_{f} (α, \infty)$ -spaces

Heikki Apiola (1983)

Compositio Mathematica

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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...