International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 2, Pages 227-232

Uniform Toeplitz matrices

I. J. Maddox

Department of Pure Mathematics, Queen's University of Belfast, Belfast BT7 1NN, Ireland

Received 19 October 1988

Copyright © 1990 I. J. Maddox. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We characterize all infinite matrices of bounded linear operators on a Banach space which preserve the limits of uniformly convergent sequences defined on an infinite set. Also, we give a Tauberian theorem for uniform summability by the Kuttner-Maddox matrix.