Let $H$ be a [Hilbert space](/page/Hilbert%20Space) and let $M \subseteq \mathcal{L}(H)$ be a type I factor von Neumann algebra. Then there exists a Hilbert space $K$ and a normal $*$-isomorphism
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\begin{align*}
M \cong \mathcal{L}(K),
\end{align*}
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where $\mathcal{L}(K)$ denotes the von Neumann algebra of bounded linear operators on $K$. Moreover, the Hilbert-space dimension of $K$ is uniquely determined by $M$.