  The infinitesimal generator $A$ of a strongly continuous semigroup on a
Hilbert space is assumed to satisfy that $B_\beta:=A-\beta$ is a sectorial
operator of angle less than $\frac{\pi}{2}$ for some $\beta \geq 0$. If
$B_\beta$ is dissipative in some equivalent scalar product then the
Naimark-Arocena Representation Theorem is applied to obtain a Kre\u{\i}n space
unitary dilation of the semigroup.
