Let $M\subseteq \mathcal{L}(H)$ be a von Neumann algebra, and let $a\in M$ be a positive operator. Let $s(a)\in M$ denote the support projection of $a$. Then $s(a)$ is the smallest projection $p\in M$ such that
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\begin{align*}
pa=a=ap.
\end{align*}
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Equivalently, $s(a)$ is the smallest projection $p\in M$ such that