Abstract This paper is devoted to the study of disjoint p-limited completely continuous (d p -lcc) operators, a new class of operators naturally associated with the notion of p -limited sets in Banach lattices. We establish connections between this new class of operators with other limited-type completely continuous classes of operators on Banach lattices. A new Gelfand–Phillips-type property related to the d p -lcc operators is defined. As an application of our results, we provide necessary and sufficient conditions under which the adjoint of every positive d p -lcc operator between two given Banach lattices is also d p -lcc. We also obtain the duality results for others limited-type completely continuous operators.
Ardakani et al. (Sat,) studied this question.