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
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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
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