(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

http://img252.imageshack.us/img252/4844/56494936eo0.png [Broken]

2. relevant equations

BL = bounded linear space (or all operators which are bounded).

3. The attempt at a solution

I got for the first part:

[tex]||A||_{BL} =||tf(t)||_{\infty} \leq ||f||_{\infty} [/tex] so

[tex] ||A||_{BL} \leq 1[/tex]

In second part I have to proof that: [tex] ||A||_{BL} \geq 1 [/tex] and thus the conclusion can be drawn.

But I'm stuck at how to use the fact that E is banach. (At least that's the one thing I haven't used yet so I presume I need it for the second part)

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# Homework Help: Operator norm

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