Mapping properties of matrix summability methods

Summary Conditions on a complex matrix A are given which are necessary and sufficient for A to have the property that if x belongs to the complex linear space generated by the set of all convergent real sequences having nonnegative kth differences, then Ax belongs to the complex linear space generated by the set of all convergent real sequences having nonnegative jth differences. Entrata in Redazione il 18 giugno 1970.