On the class of positive disjoint weak $p$-convergent operators

Abstract

We introduce and study the disjoint weak $p$-convergent operators in Banach lattices, and we give a characterization of it in terms of sequences in the positive cones. As an application, we derive the domination and the duality properties of the class of positive disjoint weak $p$-convergent operators. Next, we examine the relationship between disjoint weak $p$-convergent operators and disjoint $p$-convergent operators. Finally, we characterize order bounded disjoint weak $p$-convergent operators in terms of sequences in Banach lattices.

Keywords

• $p$-convergent operator
• disjoint $p$-convergent operator
• positive schur property of order $p$
• order continuous norm
• banach lattice