A Characterization of Banach Spaces Containing l^{1}
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 weakCauchy subsequence. The proof yields that a sequence of subsets of a given set has a subsequence that is either convergent or Boolean independent.
 Publication:

Proceedings of the National Academy of Science
 Pub Date:
 June 1974
 DOI:
 10.1073/pnas.71.6.2411
 Bibcode:
 1974PNAS...71.2411R