= Multiplication operator
{title2=$M_fu=fu$}
{wiki}
For a finite almost-everywhere measurable function $f$, the multiplication operator on <L2 space> has maximal <operator domain> $D(M_f)=\{u\in L^2:fu\in L^2\}$. It is a <closed operator>: if $u_n\to u$ and $fu_n\to v$ in <L2 space>, subsequences converge almost everywhere, giving $v=fu$. Its domain is dense, since truncating a function to the sets $|f|\leq n$ approximates it in <L2 space>. If $f$ is bounded, this is a bounded <linear operator> of norm equal to the essential supremum of $|f|$.
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