The Problem of "Total Translativity" for Hausdorff Methods

The problem of the total translativity of Holder and Cesaro methods has been considered earlier by Kuttner [3]. In the present note we are concerned with the more general problem of the total translativity of Hausdorff methods and we prove that a Hausdorff method, satisfying suitable restrictions, is totally translative if, and only if, it is the Cesaro method or a trivial modification of that method.