A class of locally convex spaces without ${\mathcal {C}}$-webs

Manuel Valdivia

Displaying similar documents to “A class of locally convex spaces without $𝒞$ -webs”

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.

Absolutely convex sets in barrelled spaces

Manuel Valdivia (1971)

Annales de l'institut Fourier

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If ${A_{n}}$ is an increasing sequence of absolutely convex sets, in a barrelled space $E$ , such that $⋃_{n = 1}^{\infty} A_{n} = E$ , it is deduced some properties of $E$ from the properties of the sets of ${A_{n}}$ . It is shown that in a barrelled space any subspace of infinite countable codimension, is barrelled.

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.

Classes of barrelled spaces related with the closed graph theorem

Valdivia, M. (1981)

Portugaliae mathematica

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Closed bounded sets in inductive limits of $𝒦$ -spaces

Carlos Bosch, Jan Kučera (1993)

Czechoslovak Mathematical Journal

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Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on $ℋ (U)$

Sean Dineen (1973)

Annales de l'institut Fourier

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This article is devoted to a study of locally convex topologies on $H (U)$ (where $U$ is an open subset of the locally convex topological vector space $E$ and $H (U)$ is the set of all complex valued holomorphic functions on $E$ ). We discuss the following topologies on $H (U)$ : (a) the compact open topology $I_{0}$ , (b) the bornological topology associated with $I_{0}$ , (c) the ported topology of Nachbin $I_{ω}$ , (d) the bornological topology associated with $I_{ω}$ ; and ...

Displaying similar documents to “A class of locally convex spaces without 𝒞 -webs”

On B r -completeness

Absolutely convex sets in barrelled spaces

On suprabarrelledness of c (Ω, X).

Classes of barrelled spaces related with the closed graph theorem

Closed bounded sets in inductive limits of 𝒦 -spaces

Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on ℋ ( U )

Displaying similar documents to “A class of locally convex spaces without $𝒞$ -webs”

On $B_{r}$ -completeness

Closed bounded sets in inductive limits of $𝒦$ -spaces

Holomorphic functions on locally convex topological vector spaces. I. Locally convex topologies on $ℋ (U)$