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Kreĭn space unitary dilations of Hilbert space holomorphic semigroups
Volume 61, no. 1
(2020),
pp. 145–160
https://doi.org/10.33044/revuma.v61n1a09
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 Kreĭn space unitary dilation
of the semigroup.
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Published by the Unión Matemática Argentina |
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