Abstract:In the first note we show for a strongly continuous family of operators $(T(t))_{t\ge 0}$ that if every orbit $t\mapsto T(t)x$ is differentiable for $t>t_x$, then all orbits are differentiable for $t>t_0$ with $t_0$ independent of $x$. In the second note we give an example of an eventually differentiable semigroup which is not differentiable on the same interval in the operator norm topology.
Keywords: eventually differentiable semigroups, operator families
AMS Subject Classification: 47D06