Definition 41.1.1 (Compression).label Let $H$ be a complex Hilbert space, $K \subset H$ be a closed subspace, $P \in B(H)$ be the orthogonal projection onto $K$, $S \in B(K)$, and $T \in B(H)$, then $S$ is a compression of $T$ if $S = PT|_{K}$.
Definition 41.1.1 (Compression).label Let $H$ be a complex Hilbert space, $K \subset H$ be a closed subspace, $P \in B(H)$ be the orthogonal projection onto $K$, $S \in B(K)$, and $T \in B(H)$, then $S$ is a compression of $T$ if $S = PT|_{K}$.
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