L-Dunford-Pettis and Almost L-Dunford-Pettis Sets in Dual Banach Lattices

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Halimeh Ardakani, Manijeh Salimi, L-Dunford-Pettis and Almost L-Dunford-Pettis Sets in Dual Banach Lattices, Int. J. Anal. Appl., 16 (2) (2018), 149-161.

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Halimeh Ardakani, Manijeh Salimi

Abstract

Following the concept of L-limited sets in dual Banach spaces introduced by Salimi and Moshtaghioun, we introduce the concepts of L-Dunford-Pettis and almost L-Dunford-Pettis sets in dual Banach lattices and then by a class of operators on Banach lattices, so called disjoint Dunford-Pettis completely continuous operators, we characterize Banach lattices in which almost L-Dunford-Pettis subsets of their dual, coincide with L-Dunford-Pettis sets.

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