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A note on regular methods of summability and the Banach-Saks property

Authors: P. Erdős and M. Magidor
Journal: Proc. Amer. Math. Soc. 59 (1976), 232-234
MSC: Primary 40H05; Secondary 46B15
MathSciNet review: 0430596
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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 [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] Nelson Dunford and Jacob T. Schwartz, Linear operators. I: General theory. Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [3] Fred Galvin and Karel Prikry, Borel sets and Ramsey's theorem, J. Symbolic Logic 38 (1973), 193-198. MR 49 #2399. MR 0337630 (49:2399)

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Keywords: Regular method of summability, partition theorems
Article copyright: © Copyright 1976 American Mathematical Society

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