The classical Lumer-Phillips theorem characterizes the generators of contraction semigroups. I am looking for a similar characterization or at least a sufficient condition for a family of unbounded, linear operators $A(t)$, $t\geq 0$, to generate a propagator $U(s,t)$, $0\leq s \leq t$, of contractions. I would appreciate any hint where I could find such a result.

Thank you in advance!

The classical Lumer-Phillips theorem characterizes the generators of contraction semigroups. I am looking for a similar characterization or at least a sufficient condition for a family of unbounded, linear operators $A(t)$, $t\geq 0$, to generate a propagator $U(t,s)$, $0\leq s \leq t$, of contractions. I would appreciate any hint where I could find such a result.

Thank you in advance!