Proceedings of the National Academy of Sciences · 1974 · 477 citations · 3 references
Linear OperatorWeak-cauchy SubsequenceBanach SpaceNorm (Mathematics)Functional AnalysisProof Yields
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.
3