Re: Supremum norm derived from an inner product ?
From: David C. Ullrich (ullrich_at_math.okstate.edu)
Date: 02/27/05
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Date: Sun, 27 Feb 2005 12:21:29 -0600
On 27 Feb 2005 09:34:38 -0800, egilbae@hotmail.com wrote:
>Could the supremum norm ||f|| = sup|f(x)| on C[0,1] possibly be
>derived from an
>inner product (.,.) such that (f,f)^(1/2) = ||f|| ?
>
>I dont think I can, but how do I proove it? If I could show the
>parallelogram law does not hold for for some f and g in C[0,1] I would
>be done.
>
>That is: ||f + g||^2 + ||f - g||^2 = 2||f||^2 + 2||g||^2
>
>Can someone give me a counterexample
Did you give _any_ thought to finding a counterexample
yourself? I mean really, if you pick any two functions
f and g at random they will be a counterexample, unless
you got _very_ unlucky. What f and g did you try?
>of this or any other suggestions
>?
************************
David C. Ullrich
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