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.

Contents Full-Text PDF