Geodesic
A Ramsey Theorem with an Application to Sequences in Banach Spaces
Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 410-417

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DOI

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.
DOI : 10.4153/CMB-2011-073-5
Mots-clés : 46B15, 05D10, Banach spaces, Ramsey theory 
Service, Robert. A Ramsey Theorem with an Application to Sequences in Banach Spaces. Canadian mathematical bulletin, Tome 55 (2012) no. 2, pp. 410-417. doi: 10.4153/CMB-2011-073-5
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     title = {A {Ramsey} {Theorem} with an {Application} to {Sequences} in {Banach} {Spaces}},
     journal = {Canadian mathematical bulletin},
     pages = {410--417},
     year = {2012},
     volume = {55},
     number = {2},
     doi = {10.4153/CMB-2011-073-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-073-5/}
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