Fourie, Jan H.Zeekoei, Elroy D.2018-02-062018-02-062017Fourie, J.H. & Zeekoei, E.D. 2017. On weak-star p-convergent operators. Quaestiones mathematicae, 40(5):563-579. [https://doi.org/10.2989/16073606.2017.1301591]1607-36061727-933X (Online)http://hdl.handle.net/10394/26257https://doi.org/10.2989/16073606.2017.1301591https://www.tandfonline.com/doi/abs/10.2989/16073606.2017.1301591The purpose of this article is to introduce and study the notion of “weak* p-convergent operator”. We discuss the relationship between the weak* p-convergent operators and the p-convergent operators, a class of operators that was introduced in the paper [4] and which plays an important role in the study of the DP*-property of order p (in the paper [14]). Some new characterizations of Banach spaces with the DP*-property of order p are obtained, the p-Gelfand-Phillips property is introduced and the behaviour of weak* p-convergent operators on Banach spaces with this property (with focus on Banach lattices with the p-Gelfand-Phillips property) is investigated. In the last section of this paper, we consider the domination properties of positive p-convergent and positive weak* p-convergent operators on Banach latticesenp-Convergent operatorWeak* p-convergent operatorDP*-property of order pp-Gelfand-Phillips propertyDomination property on Banach latticesArticle