Let $H$ be a [Hilbert space](/page/Hilbert%20Space) and let $M\subseteq \mathcal{L}(H)$. Define the commutant of $M$ by
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\begin{align*}
M'=\{T\in\mathcal{L}(H): TS=ST \text{ for every } S\in M\}.
\end{align*}
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Then $M'$ is a unital subalgebra of $\mathcal{L}(H)$ and is closed in both the strong operator topology and the weak operator topology. If $M$ is self-adjoint, meaning $S^*\in M$ for every $S\in M$, then $M'$ is also self-adjoint.