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A Ramsey Theorem with an Application to Sequences in Banach Spaces

  Published:2011-04-15
 Printed: Jun 2012
  • Robert Service,
    Department of Mathematics and Statistics, University of Helsinki
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Abstract

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: Banach spaces, Ramsey theory Banach spaces, Ramsey theory
MSC Classifications: 46B15, 05D10 show english descriptions Summability and bases [See also 46A35]
Ramsey theory [See also 05C55]
46B15 - Summability and bases [See also 46A35]
05D10 - Ramsey theory [See also 05C55]
 

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