Two notes on eventually differentiable families of operators

Bárta, Tomáš. "Two notes on eventually differentiable families of operators." Commentationes Mathematicae Universitatis Carolinae 51.1 (2010): 19-24. <http://eudml.org/doc/37743>.

@article{Bárta2010,
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.},
author = {Bárta, Tomáš},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {eventually differentiable semigroups; operator families; eventually differentiable semigroup; operator family},
language = {eng},
number = {1},
pages = {19-24},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Two notes on eventually differentiable families of operators},
url = {http://eudml.org/doc/37743},
volume = {51},
year = {2010},
}

TY - JOUR
AU - Bárta, Tomáš
TI - Two notes on eventually differentiable families of operators
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 1
SP - 19
EP - 24
AB - 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.
LA - eng
KW - eventually differentiable semigroups; operator families; eventually differentiable semigroup; operator family
UR - http://eudml.org/doc/37743
ER -