Weak* almost Dunford-Pettis operators in Banach lattices

We introduce and study the class of weak* almost Dunford-Pettis operators. As an application, we characterize Banach lattices with the weak DP* property. Also, we establish some sufficient conditions under which the class of order bounded weak* almost Dunford-Pettis operator coincide with that of almost limited. Finally, we derive some interesting results.