Generalizations of L- and M-weakly compact operators

Abstract

L-and M-weakly compact operators were introduced by Meyer-Nieberg in the beginning of 70th in attempts of a diversification of the concept of weakly compact operators via imposing Banach lattice structure on the range or on the domain of operators. We investigate regularity and algebraic properties of several generalizations of L-and M-weakly compact operators from the unified point of view with main focus on almost (order) L-, M-weakly compact operators, which were introduced recently by Bouras, Lhaimer, and Moussa. We also study several disjoint sequence properties in Banach lattices: the property (d), the dual disjoint Schur property, and the disjoint Grothendieck property.