On the class of weak almost limited operators

TL;DR

This paper introduces the class of weak almost limited operators in Banach lattices, characterizes when these operators are almost limited or almost Dunford-Pettis, and explores their properties.

Contribution

It defines weak almost limited operators and provides characterizations for when such operators are almost limited or Dunford-Pettis in Banach lattices.

Findings

Characterization of pairs of Banach lattices where positive weak almost limited operators are almost limited.

Results relating weak almost limited operators to almost limited and Dunford-Pettis operators.

New insights into the structure of operators in Banach lattice theory.

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 $T:E\rightarrow F$ is almost limited (resp. almost Dunford-Pettis). As consequences, we will give some interesting results.