Weak precompactness in Banach lattices

A remark on localized weak precompactness in Banach spaces

We give a characterization of K-weakly precompact sets in terms of uniform Gateaux differentiability of certain continuous convex functions.

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...

Some results about unbounded convergences in Banach lattices

Suppose E is a Banach lattice. A net  in E is said to be unbounded absolute weak convergent ( uaw-convergent, for short) to  provided that the net  convergences to zero, weakly.  In this note, we further investigate unbounded absolute weak convergence in E. We show that this convergence is stable under passing to and   from ideals and sublattices. Compatible with un-convergenc, we show that ...

Minimal Weak Upper Gradients in Newtonian Spaces Based on Quasi-banach Function Lattices

Properties of first-order Sobolev-type spaces on abstract metric measure spaces, so-called Newtonian spaces, based on quasi-Banach function lattices are investigated. The set of all weak upper gradients of a Newtonian function is of particular interest. Existence of minimal weak upper gradients in this general setting is proven and corresponding representation formulae are given. Furthermore, t...

Weak Interpolation in Banach Spaces