A Characterization of Banach Spaces Containing l 1
- 1 June 1974
- journal article
- Published by Proceedings of the National Academy of Sciences in Proceedings of the National Academy of Sciences
- Vol. 71 (6) , 2411-2413
- https://doi.org/10.1073/pnas.71.6.2411
Abstract
It is proved that a Banach space contains a subspace isomorphic to l 1 if (and only if) it has a bounded sequence with no weak-Cauchy subsequence. The proof yields that a sequence of subsets of a given set has a subsequence that is either convergent or Boolean independent.Keywords
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