The purpose of this note is to provide a correct proof of two results recently obtained by Khabaoui et al (Some characterizations of the ideals \(E^a\) which are discrete. Rend Circ Mat Palermo II Ser 72:1325–1336, 2023). The first result concerns the domination property of the class of L-weakly completely continuous (Lwcc) operators (Theorem 3.8), while the second concerns the reciprocal duality property of this class of operators (Theorem 3.7). Additionally, we present a refinement of other results. Furthermore, we show that every lattice homomorphism (or almost interval preserving) dominated by an Lwcc operator is itself Lwcc. Finally, we investigate the compactness properties of almost interval preserving operators.
