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## Homework Statement

Consider the vector space C[a,b] of all continuous complex-valued functions f(x), x [tex]\in[/tex] [a,b]. Define a norm ||f|| sup = max{|f(x)|, x [tex]\in[/tex] [a,b]}. (Math Note: technically we want to use sup instead of max but a physicists operational definition of max is the mathematial notion of sup).

a. Show that this is a norm.

b. Show that this norm does not satisfy the parallelogram law, ||x-y|| + ||x+y|| = 2||x||[tex]^{2}[/tex] + 2||y||[tex]^{2}[/tex]. Therefore, it cannot be an inner-product norm

## Homework Equations

IF ||v|| = 0 then |v> = 0

||v1 + v2|| [tex]\leq[/tex] ||v1|| + ||v2|| (triangle inequality)

||v|| [tex]\geq[/tex] 0

||av|| = |a| ||v|| if a [tex]\in[/tex] complex

## The Attempt at a Solution

I really have no idea where to start on this. i tried to apply the rules of a norm, but i am very confused. please help.