Let be a normed vector space and a closed subspace. Show that is also closed.

I was told to try using the Hahn-Banach theorem. So I know that there exists a function such that and . Where and

However, I don't see how to use this at all.

Printable View

- Nov 28th 2009, 02:40 PMputnam120Extending to closed space
Let be a normed vector space and a closed subspace. Show that is also closed.

I was told to try using the Hahn-Banach theorem. So I know that there exists a function such that and . Where and

However, I don't see how to use this at all. - Nov 29th 2009, 12:17 AMOpalg
- Nov 29th 2009, 03:10 PMputnam120
Thanks. In the time between our post I had figured out that I would have to show that a sequence of that form converged to a point in M. However, I was stuck at that part. (I was thinking about using the fact that the bounded linear functionals separate points somehow)