Let $H$ be a [Hilbert space](/page/Hilbert%20Space), let $M \subseteq \mathcal{L}(H)$ be a von Neumann algebra, and let $p \in M$ be a nonzero projection. Then $p$ is minimal in $M$, meaning that the only projections $q \in M$ satisfying $q \le p$ are $q=0$ and $q=p$, if and only if