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Israel Journal of Mathematics

, Volume 20, Issue 3–4, pp 375–384 | Cite as

A double-dual characterization of separable Banach spaces containingl 1

  • E. Odell
  • H. P. Rosenthal
Article

Abstract

It is proved that a separable Banach spaceB contains a subspace isomorphic tol 1 if (and only if) there exists an element inB**, the double-dual ofB, which is not a weak* limit of a sequence of elements inB. ConsequentlyB contains an isomorph ofl 1 if (and only if) the cardinality ofB** is greater than that of the continuum.

Keywords

Banach Space Separable Banach Space Compact Hausdorff Space Riesz Representation Theorem Closed Linear Span 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University 1975

Authors and Affiliations

  • E. Odell
    • 1
    • 2
  • H. P. Rosenthal
    • 1
    • 2
  1. 1.The Ohio State UniversityColumbusUSA
  2. 2.The University of CaliforniaBerkeleyUSA

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