Journal of Operator Theory

Volume 54, Issue 1, Summer 2005 pp. 9-25.

Domination of semigroups associated with sectorial forms

Authors: Amir Manavi (1), Hendrik Vogt (2) and Juergen Voigt (3)
Author institution: Fachrichtung Mathematik, Technische Universitaet Dresden, D-01062 Dresden, Germany

Summary: Let $\tau$ be a closed sectorial form in a Hilbert space $H$, and let $T=(T(t); t{\ge}0)$ be the $C_0$-semi\-group associated with $\tau$. We generalize a criterion of Ouhabaz on $T$-invariance of a closed convex set $C\subseteq H$ in terms of $\tau$ and the Hilbert space projection onto $C$. Using this criterion, we generalize known criteria for domination properties between two $C_0$-semi\-groups associated with closed sectorial forms in $L_2$-spaces. Following recent developments, the dominated semigroup is assumed to act on a Hilbert space valued $L_2$-space.

Keywords: Sectorial forms, positivity, domination, semigroups, invariance.

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