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Baire-like spaces C(X,E)

Jerzy Kakol (2000)

Revista Matemática Complutense

We characterize Baire-like spaces Cc(X,E) of continuous functions defined on a locally compact and Hewitt space X into a locally convex space E endowed with the compact-open topology.

Ball remotal subspaces of Banach spaces

Pradipta Bandyopadhyay, Bor-Luh Lin, T. S. S. R. K. Rao (2009)

Colloquium Mathematicae

We study Banach spaces X with subspaces Y whose unit ball is densely remotal in X. We show that for several classes of Banach spaces, the unit ball of the space of compact operators is densely remotal in the space of bounded operators. We also show that for several classical Banach spaces, the unit ball is densely remotal in the duals of higher even order. We show that for a separable remotal set E ⊆ X, the set of Bochner integrable functions with values in E is a remotal set in L¹(μ,X).

Banach-Saks property in some Banach sequence spaces

Yunan Cui, Henryk Hudzik, Ryszard Płuciennik (1997)

Annales Polonici Mathematici

It is proved that for any Banach space X property (β) defined by Rolewicz in [22] implies that both X and X* have the Banach-Saks property. Moreover, in Musielak-Orlicz sequence spaces, criteria for the Banach-Saks property, the near uniform convexity, the uniform Kadec-Klee property and property (H) are given.

Barrelled spaces with Boolean rings of projections.

Lech Drewnowski (1997)

Collectanea Mathematica

The talk presented a survey of results most of which have been obtained over the last several years in collaboration with M.Florencio and P.J.Paúl (Seville). The results concern the question of barrelledness of locally convex spaces equipped with suitable Boolean algebras or rings of projections. They are particularly applicable to various spaces of measurable vector valued functions. Some of the results are provided with proofs that are much simpler than the original ones.

Barrelledness of generalized sums of normed spaces

Ariel Fernández, Miguel Florencio, J. Oliveros (2000)

Czechoslovak Mathematical Journal

Let ( E i ) i ∈ I be a family of normed spaces and λ a space of scalar generalized sequences. The λ -sum of the family ( E i ) i ∈ I of spaces is λ { ( E i ) i ∈ I } : = { ( x i ) i ∈ I , x i ∈ E i , and ( ∥ x i ∥ ) i ∈ I ∈ λ } . Starting from the topology on λ and the norm topology on each E i , a natural topology on λ { ( E i ) i ∈ I } can be defined. We give conditions for λ { ( E i ) i ∈ I } to be quasi-barrelled, barrelled or locally complete.

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