| Title:
|
Two notes on eventually differentiable families of operators (English) |
| Author:
|
Bárta, Tomáš |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
19-24 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
eventually differentiable semigroups |
| Keyword:
|
operator families |
| MSC:
|
47D06 |
| idZBL:
|
Zbl 1222.47066 |
| idMR:
|
MR2666077 |
| . |
| Date available:
|
2010-05-21T12:30:33Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140085 |
| . |
| Reference:
|
[1] Bárta T.: On smooth solutions of Volterra equations via semigroups.Bull. Austral. Math. Soc. 78 (2008), 249–260. MR 2466862, 10.1017/S0004972708000683 |
| Reference:
|
[2] Batty C.J.K.: Differentiability of perturbed semigroups and delay semigroups.Perspectives in Operator Theory, 39–53, Banach Center Publ., 75, Polish Acad. Sci., Warsaw, 2007. Zbl 1126.47037, MR 2336710 |
| Reference:
|
[3] Iley P.: Perturbations of differentiable semigroups.J. Evol. Equ. 7 (2007), no. 4, 765–781. Zbl 1160.47037, MR 2369679, 10.1007/s00028-007-0349-0 |
| Reference:
|
[4] Pazy A.: Semigroups of Linear operators and Applications to Partial Differential Equations.Springer, Berlin, 1983. Zbl 0516.47023, MR 0710486 |
| . |
