Kadison's similarity theorem through uniform derivation estimates

We prove that every bounded complex-linear unital algebra homomorphism from a unital complex $C^*$-algebra into the bounded operators on an arbitrary Hilbert space is similar to a $*$-homomorphism. This resolves Kadison's similarity conjecture positively. We also obtain one universal hyperreflexivity constant for all unital von Neumann algebras on arbitrary complex Hilbert spaces.