- #1
Euge
Gold Member
MHB
POTW Director
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Here is this week's POTW:
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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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Remember to read the https://mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to https://mathhelpboards.com/forms.php?do=form&fid=2!
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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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Remember to read the https://mathhelpboards.com/showthread.php?772-Problem-of-the-Week-%28POTW%29-Procedure-and-Guidelines to find out how to https://mathhelpboards.com/forms.php?do=form&fid=2!