Definition 45.2.1 (Induced von Neumann Algebra).label Let $H$ be a complex Hilbert space, $M \subset B(H)$ be a von Neumann algebra, and $q \in \text{Proj}(M')$, then $Mq$ is a von Neumann algebra on $qH$, known as the induced von Neumann algebra of $M$ with respect to $q$.