A double-dual characterization of separable Banach spaces containingl1

@article{Odell1975ADC,
  title={A double-dual characterization of separable Banach spaces containingl1},
  author={E. Odell and H. P. Rosenthal},
  journal={Israel Journal of Mathematics},
  year={1975},
  volume={20},
  pages={375-384}
}
  • E. Odell, H. P. Rosenthal
  • Published 1975
  • Mathematics
  • Israel Journal of Mathematics
  • It is proved that a separable Banach spaceB contains a subspace isomorphic tol1 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 ofl1 if (and only if) the cardinality ofB** is greater than that of the continuum. 

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