Two notes on eventually differentiable families of operators

Abstract

In the fi rst note we show for a strongly continuous family of operators T that if every orbit t -> T(t)x is di fferentiable for t > t(x), then all orbits are di erentiable for t > t0 with t0 independent of x. In the second note we give an example of an eventually diff erentiable semigroup which is not diff erentiable on the same interval in the operator norm topology.

Keywords

• differentiable semigroups
• operator families