Krein space unitary dilations of Hilbert space holomorphic semigroups

Abstract

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.