Geodesic
Two notes on eventually differentiable families of operators
Commentationes Mathematicae Universitatis Carolinae, Tome 51 (2010) no. 1, pp. 19-24 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     author = {B\'arta, Tom\'a\v{s}},
     title = {Two notes on eventually differentiable families of operators},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {19--24},
     year = {2010},
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}
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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/