Re: Continuous differentiation

From: Lynn Kurtz (kurtzDELETE-THIS_at_asu.edu)
Date: 03/13/05 

Date: Sun, 13 Mar 2005 20:28:12 GMT

On Sat, 12 Mar 2005 23:16:48 +0000, José Carlos Santos
<jcsantos@fc.up.pt> wrote:

>José Carlos Santos wrote:
>
>> I'm posting here a problem which I've found at another newsgroup.
>> Consider the space C([0,1]) endowed with the sup norm and let F be a
>> closed vector subspace such that for each element f of F, f' is
>> continuous. Define D:F ---> C([0,1]) by D(f) = f'. Prove that D is
>> continuous.
>
>Forget about it. I've found an answer elsewhere. It's a simple
>application of the closed graph theorem.
>
>Best regards,
>
>Jose Carlos Santos

If f_n = x^n, then || f^n || = 1 and || D( f_n) || = || n x^(n - 1)||

= n so D is linear and unbounded. What am I missing?

--Lynn

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