Some characterizations of weakly compact operator on Banach lattices
We establish necessary and sufficient conditions under which each operator between Banach lattices is weakly compact and we give some consequences.
On the class of b-L-weakly and order M-weakly compact operators
In this paper, we introduce and study new concepts of b-L-weakly and order M-weakly compact operators. As consequences, we obtain some characterizations of KB-spaces.
On the class of order Dunford-Pettis operators
We characterize Banach lattices and on which the adjoint of each operator from into which is order Dunford-Pettis and weak Dunford-Pettis, is Dunford-Pettis. More precisely, we show that if and are two Banach lattices then each order Dunford-Pettis and weak Dunford-Pettis operator from into has an adjoint Dunford-Pettis operator from into if, and only if, the norm of is order continuous or has the Schur property. As a consequence we show that, if and are two Banach...
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