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Prove or disprove the following assertions for a linear map $C$ from a Banach space $X$ into itself:

a) If C is compact then its spectral radius equals the maximum of the absolute value of $C$

Im not sure what the definition of absolute value of an operator is. But the spectral value is defined as $|\sigma(M)| = max_{\lambda \in \sigma(M)} |\lambda|$

edit: I splitt it up to two questions

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I can't make sense of the question, and you also don't know what it means. Where did it come from? – Jonas Meyer Dec 12 '12 at 15:23
An old exam, maybe there was a miss print. – Johan Dec 12 '12 at 16:09

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