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Keywords:
$p$-convergent operator; disjoint $p$-convergent operator; positive Schur property of order $p$; order continuous norm; Banach lattice
$p$-convergent operator; disjoint $p$-convergent operator; positive Schur property of order $p$; order continuous norm; Banach lattice
Summary:
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.
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