We establish necessary and sufficient conditions under which b-weakly compact operators between Banach lattices have b-weakly compact adjoints or operators with b-weakly compact adjoints are themselves b-weakly compact. Also, we give some consequences.
Mathematics Subject Classification (2000). 46A40, 46B40, 46B42.
We study some properties of almost Dunford-Pettis operators and we characterize pairs of Banach lattices for which the adjoint of an almost DunfordPettis operator inherits the same property and look at conditions under which an operator is almost Dunford-Pettis whenever its adjoint is.
We introduce the class of Banach lattices with the AM-compactness property and we use it to characterize Banach lattices on which each positive weak Dunford–Pettis operator is almost Dunford–Pettis and conversely.
We characterize (L) sets and almost (L) sets in Banach lattices. Also, we look at Banach lattices in which these two classes of sets coincide. (2010): 46A40, 46B40, 46B42.
Mathematics Subject Classification
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