The duality problem for the class of b-weakly compact operators
Let \(E\) be a Banach lattice and let \(E^{\sim}\) be the order dual of \(E\). Assume that \(E^{\sim}\) separates \(E\). A subset \(U\) of \(E\) is b-order bounded provided that \(A\) is bounded in the second order dual \(E^{\sim\sim}\). If \(X\) is a Banach space and \(T:E\to X\) carries each b-order bounded subset of \(E\) into a weakly compact subset of \(X\), then \(T\) is called weakly b-order compact. The authors study the interrelation between the weak-b-order compactness of an operator and its dual.
scientific article; zbMATH DE number 5641602