Steinhaus type theorems for summability matrices-Reference-Cited by-同舟云学术

Steinhaus type theorems for summability matrices

Published:1974 Issue:2 Volume:45 Page:209-213
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Maddox I. J.

Abstract

Necessary and sufficient conditions are given for an infinite matrix to sum all bounded strongly summable sequences. It is shown that the Borel matrix does not sum all such sequences. A corollary is that the bounded summability field of the Borel method is strictly contained in that of the ( C , 1 ) (C,1) method. Also, it is proved that no coregular matrix can almost sum all bounded sequences—a generalization of Steinhaus’ theorem.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1974-045-02/S0002-9939-1974-0364938-0/S0002-9939-1974-0364938-0.pdf

Reference7 articles.

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4. A contribution to the theory of divergent sequences;Lorentz, G. G.;Acta Math.,1948

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