Absolutely convex sets in barrelled spaces

Manuel Valdivia

Displaying similar documents to “Absolutely convex sets in barrelled spaces”

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.

A class of locally convex spaces without $𝒞$ -webs

Manuel Valdivia (1982)

Annales de l'institut Fourier

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In this article we give some properties of the tensor product, with the $ϵ$ and $π$ topologies, of two locally convex spaces. As a consequence we prove that the theory of M. de Wilde of the closed graph theorem does not contain the closed graph theorem of L. Schwartz.

On certain barrelled normed spaces

Manuel Valdivia (1979)

Annales de l'institut Fourier

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Let $𝒜$ be a $σ$ -algebra on a set $X$ . If $A$ belongs to $𝒜$ let $e (A)$ be the characteristic function of $A$ . Let $ℓ_{0}^{\infty} (X, 𝒜$ be the linear space generated by ${e (A) : A \in 𝒜}$ endowed with the topology of the uniform convergence. It is proved in this paper that if $(E_{n})$ is an increasing sequence of subspaces of $ℓ_{0}^{\infty} (X, 𝒜)$ covering it, there is a positive integer $p$ such that $E_{p}$ is a dense barrelled subspace of $ℓ_{0}^{\infty} (X, 𝒜)$ , and some new results in measure theory are deduced from this fact.

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.

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 $R^{m}$ .

On the ideal of all subsets on N of ddensity zero

J.C. Ferrando, M. López Pellicer (1998)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

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In this note we obtainsome strong barrelledness properties concerning the simple function space generated by the hereditary ring Z of a11 subsets of density zero of N.

Displaying similar documents to “Absolutely convex sets in barrelled spaces”

On B r -completeness

A class of locally convex spaces without 𝒞 -webs

On certain barrelled normed spaces

On suprabarrelledness of c (Ω, X).

The space D ( U ) is not B r -complete

On the ideal of all subsets on N of ddensity zero

On $B_{r}$ -completeness

A class of locally convex spaces without $𝒞$ -webs

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