The strong BD property in Banach lattices
Abstract
We introduce the concept of strong BD property in Banach lattices and we characterize Banach lattices with this property. Also, by introducing the class of almost limited (resp. Dunford-Pettis) weakly completely continuous operators from an arbitrary Banach lattice $E$ to another $F$, we give some properties of them related to some well known classes of operators and related to the strong BD (resp. RDP$^*$) property of the Banach lattice $E$.
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