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International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 511-516

Noninclusion theorems for summability matrices

Department of Mathematics and Computer Science, Kent State University, Kent 44242, Ohio, USA

Received 30 November 1995

Copyright © 1997 Hindawi Publishing Corporation. 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.


For both ordinary convergence and 1-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.