  We introduce and study a new class of operators that we call disjoint weak
Banach-Saks operators. We establish some characterizations of this class of
operators by different types of convergence (norm convergence, unbounded order
convergence, unbounded norm convergence and unbounded absolute weak
convergence) as well as by the positive weakly null sequences. Consequently, we
give a new characterization of the disjoint weak Banach-Saks property by the
positive disjoint weakly null sequences. Furthermore, we study the relationship
between this class and other classes of operators.
