Sequentially Right-Like Properties on Banach Spaces

In this paper, we study first the concept of p-sequentially Right property, which is p-version of the sequentially Right property. Also, we introduce a new class of subsets of Banach spaces which is called p-Right* set and obtain the relationship between p-Right subsets and p-Right subsets of dual spaces. Furthermore, for 1 <= p < q <= infinity, we introduce the concepts of properties (SR)(p,q) and (SR*)(p,q) in order to find a condition such that every Dunford-Pettis q-convergent operator is Dunford-Pettis p-convergent. Finally, we apply these concepts and obtain some characterizations of the p-Dunford-Pettis relatively compact property of Banach spaces and their dual spaces.