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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 barrelled topological modules.

Pombo, Dinamérico P.jun. (1996)

International Journal of Mathematics and Mathematical Sciences

On certain barrelled normed spaces

Manuel Valdivia (1979)

Annales de l'institut Fourier

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 decomposition in barrelled spaces

P. K. Kamthan, S. K. Ray (1975)

Colloquium Mathematicae

On exhaustive vector measures.

Ferrando, Juan Carlos, López-Pellicer, Manuel (1994)

Revista Colombiana de Matemáticas

On final topologies.

Manuel Valdivia (1971)

Journal für die reine und angewandte Mathematik

On Inductive Limits of Banach Spaces.

Manuel Valdivia (1975)

Manuscripta mathematica

On linearly topologized spaces and $μ$ -spaces

Sánchez Ruiz, L.M., López Pellicer, M. (1991)

Portugaliae mathematica

On Locally Convex Spaces Ordered by a Basis.

J.T. Marti (1971)

Mathematische Annalen

On nonbornological barrelled spaces

Manuel Valdivia (1972)

Annales de l'institut Fourier

If $E$ is the topological product of a non-countable family of barrelled spaces of non-nulle dimension, there exists an infinite number of non-bornological barrelled subspaces of $E$ . The same result is obtained replacing “barrelled” by “quasi-barrelled”.

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On a Barrelled Space of Class ... and Measure Theory.

On a Class of Quasi-barrelled Spaces.

On a class of reflexive spaces related to Ulam's conjecture on measurable cardinals.

On a result of Adasch and Ernst.

On $B_{r}$ -completeness

On barrelled topological modules.

On certain barrelled normed spaces

On decomposition in barrelled spaces

On exhaustive vector measures.

On final topologies.

On Inductive Limits of Banach Spaces.

On linearly topologized spaces and $μ$ -spaces

On Locally Convex Spaces Ordered by a Basis.

On nonbornological barrelled spaces

On polynomially semibornological locally convex spaces

On Quasibarrelled Spaces.

On reducibility of some operator semigroups and algebras on locally convex spaces.

On Schwartz Spaces and Mackey Convergence

On some classes of linear topological spaces

On some classes of linear topological spaces II

Currently displaying 1 – 20 of 37