A Ramsey Theorem with an Application to Sequences in Banach Spaces

Canadian mathematical bulletin

Robert Service¹ 

[1] Department of Mathematics and Statistics, University of Helsinki

关键词: Banach spaces;    Ramsey theory;   

DOI  :  10.4153/CMB-2011-073-5

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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 isalso sketched, using the Galvin-Prikry theorem.

【 授权许可】

Unknown