A study of reciprocal Dunford-Pettis-like properties on Banach spaces

Abstract: In this article, we study the relationship between (p)-((V)) subsets and p-(V^*) subsets of dual spaces. We investigate the Banach space X with the property that adjoint every (p)-convergent operator (T: X \rightarrow Y) is weakly (q)-compact, for every Banach space (Y). Moreover, we define the notion of (q)-reciprocal Dunford-Pettis(^*)property of order (p) on Banach spaces and obtain a characterization of Banach spaces with this property. The stability of reciprocal Dunford-Pettis property of order (p) for the projective tensor product is given.