a banach space "x" has the dunford–pettis property if every continuous weakly compact operator "t": "x" → "y" from "x" into another banach space "y" transforms weakly compact sets in "x" into norm-compact sets in "y" (such operators are called completely continuous). an important equivalent definition is that for any weakly convergent sequences ("x") of "x" and ("f") of the dual space "x", converging (weakly) to "x" and "f", the sequence "f"("x") converges to "f(x)".