Noninclusion theorems for summability matrices - J. A. Fridy (International Journal of Mathematics and Mathematical Sciences)
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.