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


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.


Banach Space Separable Banach Space Compact Hausdorff Space Riesz Representation Theorem Closed Linear Span 
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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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