On the class of weak almost limited operators

Abstract

We introduce and study the class of weak almost limited operators. We establish a characterization of pairs of Banach lattices E, F for which every positive weak almost limited operator T : E → F is almost limited (resp. almost Dunford-Pettis). As consequences, we will give some interesting results.

Keywords: Weak almost limited operator, almost limited operator, almost Dunford-Pettis operator, wDP* property, almost limited set