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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Steinhaus type theorems for summability matrices
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by I. J. Maddox PDF
Proc. Amer. Math. Soc. 45 (1974), 209-213 Request permission

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 $(C,1)$ method. Also, it is proved that no coregular matrix can almost sum all bounded sequences—a generalization of Steinhaus’ theorem.
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 45 (1974), 209-213
  • MSC: Primary 40C05; Secondary 40G10
  • DOI: https://doi.org/10.1090/S0002-9939-1974-0364938-0
  • MathSciNet review: 0364938