A Characterization of Banach Spaces Containing l1
Abstract
It is proved that a Banach space contains a subspace isomorphic to l1 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.
- Publication:
-
Proceedings of the National Academy of Science
- Pub Date:
- June 1974
- DOI:
- 10.1073/pnas.71.6.2411
- Bibcode:
- 1974PNAS...71.2411R