Barreledness of subspaces of countable codimension and the closed graph theorem

D. Van Dulst

Displaying similar documents to “Barreledness of subspaces of countable codimension and the closed graph theorem”

The space $D (U)$ is not $B_{r}$ -complete

Manuel Valdivia (1977)

Annales de l'institut Fourier

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Certain classes of locally convex space having non complete separated quotients are studied and consequently results about $B_{r}$ -completeness are obtained. In particular the space of L. Schwartz $D (Ω)$ is not $B_{r}$ -complete where $Ω$ denotes a non-empty open set of the euclidean space $R^{m}$ .

Resolution of identity in certain metrizable locally convex spaces.

M. Valdivia (1989)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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Remarks on independent sequences and dimension in topological linear spaces.

Z. Lipecki (1998)

Collectanea Mathematica

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On $B_{r}$ -completeness

Manuel Valdivia (1975)

Annales de l'institut Fourier

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In this paper it is proved that if ${E_{n}}_{n = 1}^{\infty}$ and ${F_{n}}_{n = 1}^{\infty}$ are two sequences of infinite-dimensional Banach spaces then $H = (\oplus_{n = 1}^{\infty} E_{n}) \times \prod_{n = 1}^{\infty} F_{n}$ is not $B_{r}$ -complete. If ${E_{n}}_{n = 1}^{\infty}$ and ${F_{n}}_{n = 1}^{\infty}$ are also reflexive spaces there is on $H$ a separated locally convex topology $ℱ$ , coarser than the initial one, such that $H [ℱ]$ is a bornological barrelled space which is not an inductive limit of Baire spaces. It is given also another results on $B_{r}$ -completeness and bornological spaces.

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.

Some properties of $l_{p}$ ,0 < p < 1

W. Stiles (1972)

Studia Mathematica

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Abstract sliding hump technique and characterization of barrelled spaces

Dominikus Noll, Wolfgang Stadler (1989)

Studia Mathematica

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The space of countably simple bounded functions with values in a DF-space.

S. Díaz, A. Fernández, M. Florencio, P. J. Paúl (1994)

Revista Matemática de la Universidad Complutense de Madrid

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On suprabarrelledness of c (Ω, X).

Manuel López Pellicer, Salvador Moll (2003)

RACSAM

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Si Ω es un conjunto no vacío y X es un espacio normado real o complejo, se tiene que, con la norma supremo, el espacio c₀ (Ω, X) formado por las funciones f : Ω → X tales que para cada ε > 0 el conjunto {ω ∈ Ω : || f(ω) || > ε} es finito es supratonelado si y sólo si X es supratonelado.