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- Jun 20, 2014

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1. Show that if $G$ is an abelian group and $p$ is a prime such that $px = 0$ for all $x\in G$, then $G$ has the structure of a vector space over $\Bbb Z/p\Bbb Z$.

2. If $S$ is a bounded linear operator on a Banach space $X$, show that the spectral radius of $S$ is the infimum of $\|S^n\|^{1/n}$, as $n$ ranges over the positive integers.

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