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 Pelczynski'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.

中文翻译：

---

p-收敛算子和 p-Schur 性质

在本文中，我们根据对偶空间的 p-(V) 子集获得了两个 Banach 空间之间的 p-收敛算子类的特征。此外，对于 1 ≤ p < q ≤ ∞，通过引入 Pelczynski 性质 (V)p,q 和 (V*)p,q 的概念，我们获得了确保 q-收敛算子是 p-收敛算子的条件。推导出了 Banach 空间及其对偶空间的 p-Schur 性质的一些表征。