Two classes of operators related to positively limited sets on Banach lattices

Abstract

This paper is devoted to two classes of operators related to positively limited sets on Banach lattices, which we call positively limited operators and positively limited completely continuous operators, respectively. We study the relationship between these two classes of operators and other known classes of operators such as (L-, M-) weakly compact operators, almost limited operators, etc. Some lattice-topological properties of Banach lattices, the positive GP and the dual positive Schur property, are characterized in terms of positively limited operators or positively limited completely continuous operators.