On the Consistency Theorem in Matrix Summability

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Oct 1972Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 35, page 416 (issn: 0002-9939,

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Authors: Atalla, Robert E.;

doi: 10.2307/2037620 , 10.1090/s0002-9939-1972-0308640-8

On the Consistency Theorem in Matrix Summability

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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.

Keywords

Matrix methods for summability, Summability and bounded fields of methods, Inclusion and equivalence theorems in summability theory

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