Lemma 37.2.2.label Let $H$ be a complex Hilbert space, $M \subset H$ be a closed subspace, $P \in B(H)$ be the orthogonal projection onto $M$, and $T \in B(H)$, then the following are equivalent:
- (1)
$T(M) \subset M$.
- (2)
$PTP = TP$.
Lemma 37.2.2.label Let $H$ be a complex Hilbert space, $M \subset H$ be a closed subspace, $P \in B(H)$ be the orthogonal projection onto $M$, and $T \in B(H)$, then the following are equivalent:
$T(M) \subset M$.
$PTP = TP$.
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