Czechoslovak Mathematical Journal, first online, pp. 1-9
On the duality of Dunford-Pettis operators on Banach lattices
Belmesnaoui Aqzzouz, Aziz Elbour, Othman Aboutafail
Received June 27, 2011. Published online December 18, 2024.
Abstract: We establish sufficient conditions for the duality of regular Dunford-Pettis operators on Banach lattices and necessary conditions for the duality condition "if the adjoint of a (positive) operator is Dunford-Pettis, then the operator itself is". In particular, we show that if each operator $T\colon E\rightarrow F$ from a Banach lattice $E$ with an order continuous norm to another Banach lattice $F$ is Dunford-Pettis whenever its adjoint $T^{\prime}\colon F^{\prime}\rightarrow E^{\prime}$ is Dunford-Pettis, then $E$ has the Schur property or $F$ is a KB-space. As consequences, we deduce a characterization of the Schur property (and KB-spaces).
Keywords: Dunford-Pettis operator; order continuous norm; positive Schur property; KB-space
Affiliations: Belmesnaoui Aqzzouz (corresponding author), Université Mohammed V-Souissi, Faculté des Sciences Economiques, Juridiques et Sociales, Département d'Economie, B.P. 5295, SalaAljadida, Morocco, e-mail: baqzzouz@hotmail.com; Aziz Elbour, Department of Mathematics, Faculty of Sciences and Technologies, Moulay Ismail University of Meknes, 52000 Errachidia, Morocco, e-mail: azizelbour@hotmail.com; Othman Aboutafail, Engineering Sciences Laboratory, ENSA, Université Ibn Tofail, B.P. 14000, Kenitra, Morocco, e-mail: moulayothman.aboutafail@uit.ac.ma
