  We say that a $C^*$-algebra $\mathcal{A}$ satisfies the similarity property
((SP)) if every bounded homomorphism $u\colon \mathcal{A} \to
\mathcal{B}(\mathit{H})$, where $\mathit{H}$ is a Hilbert space, is similar to
a $*$-homomorphism. We introduce the following hypothesis (EP). (EP): Every
separably acting von Neumann algebra with a cyclic vector is hyperreflexive. We
prove that under (EP), all $C^*$-algebras satisfy (SP).
