Some characterizations of almost Dunford-Pettis operators and applications (Q655989)

An operator \(T\) from a Banach lattice \(E\) into a Banach space \(X\) is called almost Dunford-Pettis if \(||T(x_n)||\) converges to zero for each weakly null sequence \((x_n)\) of pairwise disjoint elements in \(E\). In their main theorem, the authors give a characterization of almost Dunford-Pettis operators. Then they give some interesting and useful corollaries to their theorem. As an application, they generalize some results on the duality between semi-compact and order weakly compact operators.