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

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 the adjoint of every p-convergent operator T : X -> 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. Also, the stability of reciprocal Dunford-Pettis property of order p for projective tensor product is given.