Revista de la
Unión Matemática Argentina
Kreĭn space unitary dilations of Hilbert space holomorphic semigroups
Stefania A. M. Marcantognini
Volume 61, no. 1 (2020), pp. 145–160

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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 Kreĭn space unitary dilation of the semigroup.