Let $H$ be a [Hilbert space](/page/Hilbert%20Space), let $M \subseteq \mathcal{L}(H)$ be a von Neumann algebra with center $Z(M)$, and let $p \in \mathcal{P}(M)$ be a projection. There exists a unique projection $c(p) \in \mathcal{P}(Z(M))$ such that $p \le c(p)$ and, for every projection $q \in \mathcal{P}(Z(M))$ with $p \le q$, one has $c(p) \le q$. This projection is called the central carrier of $p$. Moreover, for every projection $z \in \mathcal{P}(Z(M))$, $zp=0$ if and only if $zc(p)=0$.