On the consistency theorem in matrix summability

Atalla, Robert E.

doi:10.1090/S0002-9939-1972-0308640-8

On the consistency theorem in matrix summability
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by Robert E. Atalla PDF

Proc. Amer. Math. Soc. 35 (1972), 416-422 Request permission

Abstract:

We give a generalization of the consistency theorem for bounded convergence fields. The space c of convergent sequences is replaced by a space of more general type. Applications of the generalized consistency theorem are made to multiplicative summability theory. In particular we give conditions under which a generalized convergence field is an algebra.

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