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A Ramsey Theorem with an Application to Sequences in Banach Spaces

Published online by Cambridge University Press:  20 November 2018

Robert Service
Robert Service*
Affiliation:
Department of Mathematics and Statistics, University of Helsinkie-mail: [email protected]
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Abstract

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The notion of a maximally conditional sequence is introduced for sequences in a Banach space. It is then proved using Ramsey theory that every basic sequence in a Banach space has a subsequence which is either an unconditional basic sequence or a maximally conditional sequence. An apparently novel, purely combinatorial lemma in the spirit of Galvin's theorem is used in the proof. An alternative proof of the dichotomy result for sequences in Banach spaces is also sketched, using the Galvin–Prikry theorem.

Keywords

46B1505D10Banach spacesRamsey theory
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 2 , 01 June 2012 , pp. 410 - 417
Copyright
Copyright © Canadian Mathematical Society 2012

References

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