The space $D(U)$ is not $B_r$-complete

Manuel Valdivia

Displaying similar documents to “The space $D (U)$ is not $B_{r}$ -complete”

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.

Some characterizations of ultrabornological spaces

Manuel Valdivia (1974)

Annales de l'institut Fourier

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Let $U$ be an infinite-dimensional separable Fréchet space with a topology defined by a family of norms. Let $F$ be an infinite-dimensional Banach space. Then $F$ is the inductive limit of a family of spaces equal to $E$ . The choice of suitable classes of Fréchet spaces allows to give characterizations of ultrabornological spaces using the result above.. Let $Ω$ be a non-empty open set in the euclidean $n$ -dimensional space $R^{n}$ . Then $F$ is the inductive limit of a family of spaces equal to $D (Ω)$ . ...

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

W. Stiles (1972)

Studia Mathematica

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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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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 ...

A lifting theorem for locally convex subspaces of $L_{0}$

R. Faber (1995)

Studia Mathematica

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We prove that for every closed locally convex subspace E of $L_{0}$ and for any continuous linear operator T from $L_{0}$ to $L_{0} / E$ there is a continuous linear operator S from $L_{0}$ to $L_{0}$ such that T = QS where Q is the quotient map from $L_{0}$ to $L_{0} / E$ .

Mapping Properties of $c_{0}$

Paul Lewis (1999)

Colloquium Mathematicae

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Bessaga and Pełczyński showed that if $c_{0}$ embeds in the dual $X^{*}$ of a Banach space X, then $ℓ^{1}$ embeds as a complemented subspace of X. Pełczyński proved that every infinite-dimensional closed linear subspace of $ℓ^{1}$ contains a copy of $ℓ^{1}$ that is complemented in $ℓ^{1}$ . Later, Kadec and Pełczyński proved that every non-reflexive closed linear subspace of $L^{1} [0, 1]$ contains a copy of $ℓ^{1}$ that is complemented in $L^{1} [0, 1]$ . In this note a traditional sliding hump argument is used to establish a simple mapping property of...

Subspaces of $L_{p}$ which embed into $l_{p}$

W. B. Johnson, E. Odell (1974)

Compositio Mathematica

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Displaying similar documents to “The space D ( U ) is not B r -complete”

Displaying similar documents to “The space $D (U)$ is not $B_{r}$ -complete”