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 the adjoint of 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. Also, the stability of reciprocal Dunford–Pettis property of order p for projective tensor product is given.