Relative weak compactness of solid hulls in Banach lattices

Banach lattices with weak Dunford-Pettis property

We introduce and study the class of weak almost Dunford-Pettis operators. As an application, we characterize Banach lattices with the weak Dunford-Pettis property. Also, we establish some sufficient conditions for which each weak almost Dunford-Pettis operator is weak Dunford-Pettis. Finally, we derive some interesting results. Keywords—eak almost Dunford-Pettis operator, almost DunfordPettis o...

Weak Limits of Projections and Compactness of Subspace Lattices

A strongly closed lattice of projections on a Hubert space is compact if the associated algebra of operators has a weakly dense subset of compact operators. If the lattice is commutative, there are necessary and sufficient conditions for compactness, one in terms of the structure of the lattice, and the other in terms of a measure on the lattice. There are many examples of compact lattices, and...

Conditional and Relative Weak Compactness in Vector-Valued Function Spaces

Let E be an ideal of Lo over a σ-finite measure space (Ω,Σ, μ), and let (X, ‖ ·‖X) be a real Banach space. Let E(X) be a subspace of the space Lo(X) of μ-equivalence classes of all strongly Σ-measurable functions f : Ω −→ X and consisting of all those f ∈ Lo(X) for which the scalar function ‖f(·)‖X belongs to E. Let E(X)n stand for the order continuous dual of E(X). In this paper we characteriz...

On compactness of lattices

In this paper, we present a study of various concepts pertaining to compactness properties of a lattice. Special cases include such notions as countably compactness, almost countably compactness, and countably paracompactness. Some investigations in these matters have been done in [2, 7, 14]. We go beyond these results and introduce new subsets of I(L) and their lattices to investigate. This wa...

Weak Compactness of the Set of ε-Extensions