A norm |⋅| on a Banach space X is locally uniformly rotund (LUR) if lim |x n — x| = 0 for every x n , x ∈ X for which lim2|x|2 + 2 |x n |2-|xn+x n|2 = 0. It is shown that a Banach space X admits an equivalent LUR norm provided there is a bounded linear operator T of X into c0(Γ) such that T* c*0(Γ) is norm dense in X*. This is the case e.g. if X* is weakly compactly generated (WCG).