Re: When is V* not isomorphic to V?

David C. Ullrich wrote: 
On Sat, 3 Dec 2005 17:41:03 +0000 (UTC), kj <socyl@xxxxxxxxxxxxxxxxx>
wrote:

Is it possible for a vector space not to be isomorphic to its dual
space V*?  If so, is it possible to state necessary and sufficient
conditions for a vector space not to be isomorphic to its dual
space?  Where can I find a proof of this?

Assuming the axiom of choice, I _think_ that V* is isomorphic
to V if and only if dim(V) is finite. Not sure of this.


My first reaction to this was 'What about Hilbert spaces?'.

Is the catch that in the Hilbert space case we talk about the
space of continuous linear functionals as the dual, but
there are also the non-continuous ones to contend with?

It's something of an inconvenience that linear doesn't
imply continuous in infinite dimensions...
.

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