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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, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers, Ltd., London, 1958. MR 0117523
  • [3] Fred Galvin and Karel Prikry, Borel sets and Ramsey’s theorem, J. Symbolic Logic 38 (1973), 193–198. MR 0337630

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