On pseudo weakly compact operators of order $ P$

Abstract

In this paper, we introduce the concept of a pseudo weakly compact operator of order p between Banach spaces. Also we study the notion of p-Dunford-Pettis relatively compact property which is in "general" weaker than the Dunford-Pettis relatively compact property and gives some characterizations of Banach spaces which have this property. Moreover, by using the notion of p-Right subsets of a dual Banach space, we study the concepts of p-sequentially Right and weak p-sequentially Right properties on Banach spaces. Furthermore, we obtain some suitable conditions on Banach spaces X and Y such that projective tensor and injective tensor products between X and Y have the p-sequentially Right property. Finally, we introduce two properties for the Banach spaces, namely p-sequentially Right * and weak p-sequentially Right * properties and obtain some characterizations of these properties.