  In this paper we introduce and study a new class of operators related to norm
bounded sets on Banach Lattice and which brings together several classical
classes of operators (as o-weakly compact operators, b-weakly compact
operators, M-weakly compact operators, L-weakly compact operators, almost
Dunford-Pettis operators). As consequences, we give some new lattice
approximation properties of these classes of operators.
