p-Convergent Operators and the p-Schur Property

In this article we obtain a characterization of the class of p -convergent operators between two Banach spaces in terms of p -( V ) subsets of the dual space. Also, for 1 ≤ p < q ≤ ∞, by introducing the concepts of Pelczyński's properties ( V ) p , q and ( V *) p , q , we obtain a condition that ensures that q -convergent operators are p -convergent operators. Some characterizations of the p -Schur property of Banach spaces and their dual spaces are deduced.