Weak Unbounded Norm Topology and Dounford-Pettis Operators

Abstract

In this paper, we study un-dual (in symbol, E ⋄ ) of Banach lattice E and compare it with topological dual E * . If E * has order continuous norm, then E * = E ⋄ . We introduce and study weakly unbounded norm topology (wun-topology) on Banach lattices and compare it with weak topology and uaw-topology. In the final, we introduce and study wun-Dunford-Pettis opertors from a Banach lattice E into Banach space X and we investigate some of its properties and its relationships with others known operators.