On the class of unbounded-U-Dunford-Pettis operators

The aim of this paper is to introduce and study a new class of operators between Banach lattices based on the unbounded norm topology, nominated "unbounded-U-Dunford-Pettis operators". Namely, we give some characterizations of this class, we study the relations between this class and other classes of operators known in the literature of operator theory on Banach lattices, and we study the duality problem for this class of operators. 2010 Mathematics Subject Classification. 46B42, 47B60, 47B65.