Natural generalization of the class of ℒ∞-spaces in the category of b-spaces

A new class of b-spaces, called ε b-spaces, is defined. This class is a natural generalization of the class of ℒ_∞-spaces. Some properties of ε b-spaces are established. __________ Translated from Problemy Matematicheskogo Analiza, No. 33, 2006, pp. 3–11.     

Characterization of locally convex solid topologies of lebesgue on the vector latticeC(X)

We give some sufficient and necessary conditions such that the vector lattice of continuous functions on a compact topological space, not necessary metrizable, admits a locally convex and solid topology which is Lebesgue.

     

Sur les opérateurs précompacts positifs

We characterize complete Hausdorff locally convex solid lattices (E,τ) satisfying the following property: for all operators $\text{S,T}\text{:E→E}$ such that 0?S?T and T precompact, the operator S² is precompact. To cite this article: B. Aqzzouz, R. Nouira, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

The b-Weak Compactness of Order Weakly Compact Operators

We characterize Banach lattices on which the class of order weakly compact operators coincides with that of b-weakly compact operators.     

The Abelian category of quotients of $$\mathcal{L}\mathfrak{F}$$ -spaces

We construct the category of quotients of -spaces and we show that it is Abelian. This answers a question of L. Waelbroeck from 1990.     

The duality problem for the Class of b-weakly compact operators

We establish necessary and sufficient conditions under which b-weakly compact operators between Banach lattices have b-weakly compact adjoints or operators with b-weakly compact adjoints are themselves b-weakly compact. Also, we give some consequences.      

Semi-compactness of positive Dunford-Pettis operators on Banach lattices

We investigate Banach lattices on which each positive Dunford-Pettis operator is semi-compact and the converse. As an interesting consequence, we obtain Theorem 2.7 of Aliprantis-Burkinshaw and an element of Theorem 1 of Wickstead.