Some characterizations of almost order (L) sets and applications

The purpose of this paper is to establish several characterizations of almost order (L) sets (respectively, almost (L) sets). These characterizations generalize and correct those obtained recently by K. El Fahri and F.Z. Oughajji. In addition, we show that the almost (L) sets enjoy some interesting lattice approximation properties. Among other things, we show that a Banach lattice E has weakly sequentially continuous lattice operations if and only if the convex solid hull of every (L) set of \( E^{\prime }\) $E^{\prime }$ is an (L) set. Moreover, we study the domination property for absolutely weakly sequentially continuous operators.