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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the consistency theorem in matrix summability


Author: Robert E. Atalla
Journal: Proc. Amer. Math. Soc. 35 (1972), 416-422
MSC: Primary 40D20; Secondary 40C05
DOI: https://doi.org/10.1090/S0002-9939-1972-0308640-8
MathSciNet review: 0308640
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0308640-8
Keywords: Convergence field, inclusion theorem, consistent matrix methods, multipicative matrix method, $ \beta N$
Article copyright: © Copyright 1972 American Mathematical Society