A note on the U-Dunford-Pettis operators

AbstractThe purpose of this note is to give a correct proof of the theorem that concerns the domination property of the class of U-Dunford-Pettis operators obtained by O. Aboutafail, K. El Fahri, J. H'Michane and L. Zraoula [On the class of U-Dunford-Pettis operators, Quaestiones Mathematicae 45(4) (2022), 655–666]. Also, we investigate necessary and sufficient conditions under which U-Dunford–Pettis operators between Banach lattices must be Dunford–Pettis.Mathematics Subject Classification (2020): Primary: 46B42Secondary: 47B6047B65Key words: Dunford-Pettis operatorU-Dunford-Pettis operatorAM-compact operatororder continuous normBanach lattice