On the positive weak almost limited operators

Abstract

Using the concept of approximately order bounded sets with respect to a lattice seminorm, we establish some new characterizations of positive weak almost limited operators on Banach lattices. Consequently, we derive some results about the weak Dunford–Pettis* and the Dunford–Pettis* property of σ-Dedekind complete Banach lattices.

Keywords

• Weak almost limited operator
• The weak Dunford–Pettis* property
• Banach lattice