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 $\beta \ge 0$. If $B_{\beta }$ is dissipative in some equivalent scalar product then the Naimark-Arocena Representation Theorem is applied to obtain a Kre\uın space unitary dilation of the semigroup.