| Title:
|
Small sets and hypercyclic vectors (English) |
| Author:
|
Bayart, F. |
| Author:
|
Matheron, É. |
| Author:
|
Moreau, P. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
49 |
| Issue:
|
1 |
| Year:
|
2008 |
| Pages:
|
53-65 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study the ``smallness'' of the set of non-hypercyclic vectors for some classical hypercyclic operators. (English) |
| Keyword:
|
hypercyclic operators |
| Keyword:
|
porous sets |
| Keyword:
|
Haar-null sets |
| MSC:
|
28A05 |
| MSC:
|
47A16 |
| MSC:
|
47B37 |
| idZBL:
|
Zbl 1210.47022 |
| idMR:
|
MR2432820 |
| . |
| Date available:
|
2009-05-05T17:06:26Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119701 |
| . |
| Reference:
|
[1] Bayart F.: Porosity and hypercyclic vectors.Proc. Amer. Math. Soc. 133 (2005), 11 3309-3316. MR 2161154, 10.1090/S0002-9939-05-07842-1 |
| Reference:
|
[2] Bonilla A., Grosse-Erdmann K.-G.: Frequently hypercyclic operators and vectors.Ergodic Theory Dynam. Systems 27 (2007), 2 383-404. Zbl 1119.47011, MR 2308137 |
| Reference:
|
[3] Christensen J.P.R.: On sets of Haar measure zero in abelian Polish groups.Israel J. Math. 13 (1972), 255-260. MR 0326293, 10.1007/BF02762799 |
| Reference:
|
[4] Dolženko E.P.: Boundary properties of arbitrary functions.Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967), 3-14. MR 0217297 |
| Reference:
|
[5] Godefroy G., Shapiro J.H.: Operators with dense, invariant, cyclic vector manifolds.J. Funct. Anal. 98 (1991), 2 229-269. Zbl 0732.47016, MR 1111569, 10.1016/0022-1236(91)90078-J |
| Reference:
|
[6] Grosse-Erdmann K.-G.: Universal families and hypercyclic operators.Bull. Amer. Math. Soc. 36 (1999), 345-381. Zbl 0933.47003, MR 1685272, 10.1090/S0273-0979-99-00788-0 |
| Reference:
|
[7] Ott W., Yorke J.A.: Prevalence.Bull. Amer. Math. Soc. 42 (2005), 263-290. Zbl 1111.28014, MR 2149086, 10.1090/S0273-0979-05-01060-8 |
| Reference:
|
[8] Salas H.: Hypercyclic weighted shifts.Trans. Amer. Math. Soc. 347 (1995), 3 993-1004. Zbl 0822.47030, MR 1249890, 10.1090/S0002-9947-1995-1249890-6 |
| Reference:
|
[9] Zajíček L.: Porosity and $\sigma$-porosity.Real Anal. Exchange 13 (1987-1988), 2 314-350. MR 0943561 |
| Reference:
|
[10] Zajíček L.: Sets of $\sigma$-porosity and sets of $\sigma$-porosity $(q)$.Časopis Pěst. Mat. 101 (1976), 350-359. Zbl 0341.30026, MR 0457731 |
| . |
