Let $A$ be a unital complex C*-algebra. Then there exist a complex [Hilbert space](/page/Hilbert%20Space) $H$ and a norm-closed unital *-subalgebra $B\subset \mathcal{L}(H)$, where $\mathcal{L}(H)$ denotes the C*-algebra of bounded linear operators on $H$, such that $A$ is unital *-isomorphic to $B$. Moreover, the isomorphism may be chosen isometric: there is a unital *-isomorphism $\Phi:A\to B$ satisfying

\begin{align*} \|\Phi(a)\|_{\mathcal{L}(H)}=\|a\|_A \end{align*}

for every $a\in A$.