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

  • Thread starter DeadWolfe
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But the cannonical injection to not be an isomorphism?
 

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But the cannonical injection to not be an isomorphism?


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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