On the weak compactness of b-weakly compact operators
In this paper, the aim of the authors is to prove that each b-weakly compact operator \(T\) from a Banach lattice \(E\) into a Banach space \(X\) is weakly compact if and only if the norm of dual space \(E'\) is order continuous or \(X\) is reflexive. As a result, they give some characterizations of the order continuity of the dual norm and a characterization of reflexive Banach lattices. They also give a necessary and sufficient condition under which the second power of a b-weakly compact operator is weakly compact.
scientific article; zbMATH DE number 5692401
scientific article