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

1. May 9, 2008

But the cannonical injection to not be an isomorphism?

2. May 9, 2008

### Pere Callahan

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".