On the class of weak almost limited operators
  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. 
A. Elbour, N. Machrafi, M. Moussa
math.FA