A Characterization of Banach Spaces Containing l 1

1974/06/01 by Haskell P. Rosenthal · 13 citations
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces

paper · doi:10.1073/pnas.71.6.2411

openalex publication_date 1974/06/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/06/11

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.

Cited by

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• Examples of k-iterated spreading models
• Dividing lines in unstable theories and subclasses of Baire 1 functions
• A Coarse-Lipschitz Embedding of c₀ into a Separable Dual Banach Space
• Embedding ℓ_∞ into the space of all Operators on Certain Banach Spaces
• On the approximate fixed point property in abstract spaces
• Asymptotic structure and coarse Lipschitz geometry of Banach spaces
• Combinatorial independence and naive entropy
• BIDUAL OCTAHEDRAL RENORMINGS AND STRONG REGULARITY IN BANACH SPACES
• Banach space [wikipedia]