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We introduce new concept of almost demi Dunford–Pettis operators. Let be a Banach lattice. An operator from into is said to be almost demi Dunford–Pettis if, for every sequence in such that in and as , we have as . In addition, we study some properties of this class of operators and its relationships with others known operators.
We characterize Banach lattices on which each regular order weakly compact (resp. b-weakly compact, almost Dunford-Pettis, Dunford-Pettis) operator is AM-compact.
This paper presents an elementary proof and a generalization of a theorem due to Abramovich and Lipecki, concerning the nonexistence of closed linear sublattices of finite codimension in nonatomic locally solid linear lattices with the Lebesgue property.
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