Abstract
A bounded subset K of X is defined to be a weak reciprocal Dunford–Pettis set (or wRDP set) if T(K) is relatively weakly compact for each completely continuous operator \({T \colon X \to c_0}\). A Banach space X has the R* property if every wRDP subset of X is relatively weakly compact. In this paper we study weak reciprocal Dunford–Pettis sets and Banach spaces with property R*.
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