POSITIVELY LIMITED p -CONVERGENT AND WEAK * POSITIVELY p -CONVERGENT OPERATORS.

The purpose of this article is to study two classes of operators, which we call positively limited p-convergent operators, and weak * positively p-convergent operators. We discuss the relationship between these two classes of operators, and other known classes of operators such as p-convergent operators, limited p-convergent operators, disjoint p-convergent operators, etc. Moreover, the positive DP * property of order p is studied, and the behavior of these two classes of operators on Banach lattices with this property (with focus on Banach lattices with the positively limited p-Schur property) is investigated. In addition, the domination properties of positively limited p-convergent operators, and weak * positively p-convergent operators on Banach lattices are considered. [ABSTRACT FROM AUTHOR]