Sur une inégalité complémentaire de l'inégalité triangulaire
The functor σ²X
We disprove the existence of a universal object in several classes of spaces including the class of weakly Lindelöf Banach spaces.
The Lindelöf property and σ-fragmentability
In the previous paper, we, together with J. Orihuela, showed that a compact subset X of the product space is fragmented by the uniform metric if and only if X is Lindelöf with respect to the topology γ(D) of uniform convergence on countable subsets of D. In the present paper we generalize the previous result to the case where X is K-analytic. Stated more precisely, a K-analytic subspace X of is σ-fragmented by the uniform metric if and only if (X,γ(D)) is Lindelöf, and if this is the case then...
The Lindelöf property in Banach spaces
A topological space (T,τ) is said to be fragmented by a metric d on T if each non-empty subset of T has non-empty relatively open subsets of arbitrarily small d-diameter. The basic theorem of the present paper is the following. Let (M,ϱ) be a metric space with ϱ bounded and let D be an arbitrary index set. Then for a compact subset K of the product space the following four conditions are equivalent: (i) K is fragmented by , where, for each S ⊂ D, . (ii) For each countable subset A of D, is...
The precompactness–lemma
The range of vector measures into Orlicz spaces
The structure of Eberlein, uniformly Eberlein and Talagrand compact spaces in Σ()
Weak Cauchy sequences in
For a finite and positive measure space Ω,∑,μ characterizations of weak Cauchy sequences in , the space of μ-essentially bounded vector-valued functions f:Ω → X, are presented. The fine distinction between Asplund and conditionally weakly compact subsets of is discussed.
Weak compactness and summability
Weak compactness criteria and convergences in LE1(μ).
Weak Compactness in Locally Convex g-Spaces and Related Questions.
Weak compactness in the space of operator valued measures and its applications
In this note we present necessary and sufficient conditions characterizing conditionally weakly compact sets in the space of (bounded linear) operator valued measures . This generalizes a recent result of the author characterizing conditionally weakly compact subsets of the space of nuclear operator valued measures . This result has interesting applications in optimization and control theory as illustrated by several examples.
Weak Compactness, Pseudo-reflexivity and Quasi-reflexivity.
Weak convergence in infinite dimensional spaces
Weak countable compactness implies quasi-weak drop property
Every weakly countably compact closed convex set in a locally convex space has the quasi-weak drop property.
Weakly almost periodic vector-valued functions [Book]
Weakly c'-compact subsets of non-archimedean Banach spaces over a spherically complete field.
Zur Lototsky - Transformation über kompakten Räumen von Wahrscheinlichkeitsmassen.
Доли Глисона и граница Шоке алгебры функцций на выпуклом компакте
Некоторые замечания о свойствах операторов Рaдона-Никодима с применениями к одному вопросу М.Талаграна.