Czechoslovak Mathematical Journal, Vol. 70, No. 4, pp. 1047-1057, 2020
A note on L-Dunford-Pettis sets in a topological dual Banach space
Received March 18, 2019. Published online April 30, 2020.
Abstract: 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.