The present paper is devoted to some applications of the notion of L-Dunford-Pettis sets to several classes of operators on Banach lattices. More precisely, we establish some characterizations of weak Dunford-Pettis, Dunford-Pettis completely continuous, and weak almost Dunford-Pettis operators. Next, we study the relationships between LDunford-Pettis, and Dunford-Pettis (relatively compact) sets in topological dual Banach spaces.

中文翻译：

---

关于拓扑对偶 Banach 空间中的 L-Dunford-Pettis 集的注记

本论文致力于将 L-Dunford-Pettis 集的概念应用于 Banach 格上的几类算子。更准确地说，我们建立了弱Dunford-Pettis、Dunford-Pettis完全连续和弱几乎Dunford-Pettis算子的一些特征。接下来，我们研究拓扑对偶 Banach 空间中 LDunford-Pettis 和 Dunford-Pettis（相对紧凑）集之间的关系。