Geodesic
Two notes on eventually differentiable families of operators
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 1, pp. 19-24.

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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.
Classification : 47D06
Keywords: eventually differentiable semigroups; operator families 
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Bárta, Tomáš. Two notes on eventually differentiable families of operators. Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 1, pp. 19-24. http://geodesic.mathdoc.fr/item/CMUC_2010__51_1_a2/