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Is it possible for a Banach Space to be isomorphic to its double dual

  1. May 9, 2008 #1
    But the cannonical injection to not be an isomorphism?
     
  2. jcsd
  3. May 9, 2008 #2

    In 1950, R. C. James constructed a Banach space which is isometrically isomorphic to its bidual but not reflexive. The natural injection is thus not surjective and therefore no isomorphism.

    Reportedly, a proof can be found in Lindenstrauss/Tzafriri "Classical Banach Spaces".
     
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