International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 511-516
doi:10.1155/S0161171297000690

Noninclusion theorems for summability matrices

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.