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.
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.
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/
@article{CMUC_2010_51_1_a2,
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},
volume = {51},
number = {1},
mrnumber = {2666077},
zbl = {1222.47066},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMUC_2010_51_1_a2/}
}