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Keywords:
L-Dunford-Pettis set; weak almost Dunford-Pettis operator; weak Dunford-Pettis property; Banach lattice
L-Dunford-Pettis set; weak almost Dunford-Pettis operator; weak Dunford-Pettis property; Banach lattice
Summary:
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 L-Dunford-Pettis, and Dunford-Pettis (relatively compact) sets in topological dual Banach spaces.
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