How do you compute the unit ball of a dual norm to an induced norm on a subspace of Lp?

It's easy to figure out what the unit ball for the induced norm on a
subspace of Lp will look like: it's just the intersection of the unit
ball of Lp itself and the subspace in question.

Given that information, how does one figure out what the unit ball of
the dual norm is?

Does anyone already know an easy way to do this, or should I do some
further research?

-Mike

Anyone? Does this mean that it's not known what the general way is to do it?

-Mike

On Mon, Jul 16, 2012 at 4:58 PM, Mike Battaglia <battaglia01@gmail.com> wrote:
> It's easy to figure out what the unit ball for the induced norm on a
> subspace of Lp will look like: it's just the intersection of the unit
> ball of Lp itself and the subspace in question.
>
> Given that information, how does one figure out what the unit ball of
> the dual norm is?
>
> Does anyone already know an easy way to do this, or should I do some
> further research?
>
> -Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Anyone? Does this mean that it's not known what the general way is to do it?

I'll think about it when I have time.

Hi Mike,
I suppose the following application of Hahn-Banach's theorem could be adapted to answer your question:
http://www.math.unl.edu/~s-bbockel1/928/node25.html
Please let me know if this is fine for you.
Bests,
Claudi

Thanks Claudi! This is exactly the missing piece I was looking for.
Ironically, I spent the past few days going over Hahn-Banach, being
pointed to it by the Efnet #math people, and couldn't figure out how
to proceed from there. This is it.

I had a few related conjectures which this proves. I'll write
something up shortly about how this related to vals.

-Mike

On Thu, Jul 19, 2012 at 12:46 PM, clamengh <clamengh@yahoo.fr> wrote:
>
> Hi Mike,
> I suppose the following application of Hahn-Banach's theorem could be adapted to answer your question:
> http://www.math.unl.edu/~s-bbockel1/928/node25.html
> Please let me know if this is fine for you.
> Bests,
> Claudi

You're welcome Mike,
I am happy this was fine.
Now I should find some time and energy to understand... tuning theory itself :)
Best wishes,
Claudi