Additivity of the gauge
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.