International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 511-516
doi:10.1155/S0161171297000690
Noninclusion theorems for summability matrices
Department of Mathematics and Computer Science, Kent State University, Kent 44242, Ohio, USA
Received 30 November 1995
Copyright © 1997 J. A. Fridy. 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.
Abstract
For both ordinary convergence and ℓ1-summability explicit sufficient conditions on a
matrix have long been known that ensure that the summability method is strictly stronger than the identity
map. The main results herein show that a matrix that satisfies those conditions can be included by
another matrix only if the other matrix satisfies those same conditions.