Some characterizations of almost limited operators

摘要

In this paper we give several characterizations of almost limited operators. Mainly, it is proved that an operator T : X -> E from a Banach space X into a sigma-Dedekind complete Banach lattice E is almost limited if and only if parallel to T* (f(n))parallel to -> 0 for every positive weak* null sequence (f(n)) of E*. Moreover, we present some interesting connections between almost limited, almost Dunford-Pettis and limited operators.