Let X be a Banach space and T ∈ B(X). Cohen determined a class of regular infinite matrices A = (a nk) for which L n := ∞ k=1 a nk T k converges strongly to an element invariant under T. In the present paper we study A-mean and A-uniform ergodic type results when A = (a nk) is a regular infinite matrix satisfying Cohen's uniformity condition lim j ∞ k= j |a n,k+1 − a nk | = 0, uniformly in n.