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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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A note on regular methods of summability and the Banach-Saks property
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by P. Erdős and M. Magidor PDF
Proc. Amer. Math. Soc. 59 (1976), 232-234 Request permission

Abstract:

Using the Galvin-Prikry partition theorem from set theory it is proved that every bounded sequence in a Banach space has a subsequence such that either every subsequence of which is summable or no subsequence of which is summable.
References
    Antoine Brumel et Louis Sucheston, Sur quelques conditions equivalentes à la super-reflexivité dans les espaces de Banach, C.R. Acad. Sci. Paris 275 (1972), 993-994.
  • Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
  • Fred Galvin and Karel Prikry, Borel sets and Ramsey’s theorem, J. Symbolic Logic 38 (1973), 193–198. MR 337630, DOI 10.2307/2272055
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 59 (1976), 232-234
  • MSC: Primary 40H05; Secondary 46B15
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0430596-1
  • MathSciNet review: 0430596