| Title:
|
On the disk-cyclic linear relations (English) |
| Author:
|
Amouch, Mohamed |
| Author:
|
Ech-Chakouri, Ali |
| Author:
|
Zguitti, Hassane |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
150 |
| Issue:
|
3 |
| Year:
|
2025 |
| Pages:
|
309-330 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The study of linear dynamical systems for linear relations was initiated by C.-C. Chen et al. in (2017). Then E. Abakumov et al. extended hypercyclicty to linear relations in (2018). We extend the concept of disk-cyclicity studied in M. Amouch, O. Benchiheb (2020), Z. Z. Jamil, M. Helal (2013), Y.-X. Liang, Z.-H. Zhou (2015), Z. J. Zeana (2002) for linear operators to linear relations. (English) |
| Keyword:
|
hypercyclicity |
| Keyword:
|
linear relation |
| Keyword:
|
disk-cyclic linear relation |
| Keyword:
|
disk transitive linear relation |
| MSC:
|
37B20 |
| MSC:
|
47A06 |
| MSC:
|
47A16 |
| DOI:
|
10.21136/MB.2024.0015-24 |
| . |
| Date available:
|
2025-09-26T13:52:55Z |
| Last updated:
|
2025-09-26 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153077 |
| . |
| Reference:
|
[1] Abakumov, E., Boudabbous, M., Mnif, M.: On hypercyclicity of linear relations.Result. Math. 73 (2018), Article ID 137, 17 pages. Zbl 1507.47003, MR 3860909, 10.1007/s00025-018-0900-z |
| Reference:
|
[2] Álvarez, T.: Quasi-Fredholm and semi-B-Fredholm linear relations.Mediterr. J. Math. 14 (2017), Article ID 22, 26 pages. Zbl 1476.47003, MR 3590364, 10.1007/s00009-016-0828-z |
| Reference:
|
[3] Álvarez, T., Keskes, S., Mnif, M.: On the structure of essentially semi-regular linear relations.Mediterr. J. Math. 16 (2019), Article ID 76, 20 pages. Zbl 1499.47003, MR 3942866, 10.1007/s00009-019-1334-x |
| Reference:
|
[4] Alvarez, T., Sandovici, A.: Regular linear relations on Banach spaces.Banach J. Math. Anal. 15 (2021), Article ID 4, 25 pages. Zbl 1507.47004, MR 4159771, 10.1007/s43037-020-00092-9 |
| Reference:
|
[5] Amouch, M., Benchiheb, O.: Diskcyclicity of sets of operators and applications.Acta Math. Sin., Engl. Ser. 36 (2020), 1203-1220. Zbl 07334462, MR 4174620, 10.1007/s10114-020-9307-3 |
| Reference:
|
[6] Bamerni, N., Kiliçman, A.: Operators with diskcyclic vectors subspaces.J. Taibah Univ. Sci. 9 (2015), 414-419. 10.1016/j.jtusci.2015.02.020 |
| Reference:
|
[7] Bamerni, N., Kiliçman, A., Noorani, M. S. M.: A review of some works in the theory of diskcyclic operators.Bull. Malays. Math. Soc. 39 (2016), 723-739. Zbl 1344.47004, MR 3471344, 10.1007/s40840-015-0137-x |
| Reference:
|
[8] Bouaniza, H., Chamkha, Y., Mnif, M.: Perturbation of semi-Browder linear relations by commuting Riesz operators.Linear Multilinear Algebra 66 (2018), 285-308. Zbl 1502.47002, MR 3750591, 10.1080/03081087.2017.1298079 |
| Reference:
|
[9] Chafai, E., Mnif, M.: Ascent and essential ascent spectrum of linear relations.Extr. Math. 31 (2016), 145-167. Zbl 1381.47005, MR 3645262 |
| Reference:
|
[10] Chen, C.-C., Conejero, J. A., Kostić, M., Murillo-Arcila, M.: Dynamics of multivalued linear operators.Open Math. 15 (2017), 948-958. Zbl 1459.47002, MR 3674105, 10.1515/math-2017-0082 |
| Reference:
|
[11] Cross, R.: Multivalued Linear Operators.Pure and Applied Mathematics 213. Marcel Dekker, New York (1998). Zbl 0911.47002, MR 1631548 |
| Reference:
|
[12] Grosse-Erdmann, K.-G., Manguillot, A. Peris: Linear Chaos.Universitext. Springer, Ber-lin (2011). Zbl 1246.47004, MR 2919812, 10.1007/978-1-4471-2170-1 |
| Reference:
|
[13] Jamil, Z. Z., Helal, M.: Equivalent between the criterion and the three open set's conditions in disk-cyclicity.Int. J. Contemp. Math. Sci. 8 (2013), 257-261. Zbl 1283.47013, MR 3040831, 10.1007/978-1-4471-2170-1 |
| Reference:
|
[14] Liang, Y.-X., Zhou, Z.-H.: Disk-cyclicity and codisk-cyclicity of certain shift operators.Oper. Matrices 9 (2015), 831-846. Zbl 1347.47008, MR 3447588, 10.7153/oam-09-48 |
| Reference:
|
[15] Liang, Y.-X., Zhou, Z.-H.: Disk-cyclic and codisk-cyclic tuples of the adjoint weighted composition operators on Hilbert spaces.Bull. Belg. Math. Soc. - Simon Stevin 23 (2016), 203-215. Zbl 1384.47005, MR 3507078, 10.36045/bbms/1464710114 |
| Reference:
|
[16] Mnif, M., Neji, R.: Kato decomposition theorem for linear pencils.Filomat 34 (2020), 1157-1166. Zbl 1498.47033, MR 4205477, 10.2298/FIL2004157M |
| Reference:
|
[17] Mnif, M., Ouled-Hmed, A.-A.: Local spectral theory and surjective spectrum of linear relations.Ukr. Math. J. 73 (2021), 255-275. Zbl 07411045, MR 4223547, 10.1007/s11253-021-01920-3 |
| Reference:
|
[18] Rolewicz, S.: On orbits of elements.Stud. Math. 32 (1969), 17-22. Zbl 0174.44203, MR 0241956, 10.4064/sm-32-1-17-22 |
| Reference:
|
[19] Sandovici, A.: On the adjoint of linear relations in Hilbert spaces.Mediterr. J. Math. 17 (2020), Article ID 68, 23 pages. Zbl 1442.47001, MR 4070098, 10.1007/s00009-020-1503-y |
| Reference:
|
[20] Wang, Y., Zeng, H.-G.: Disk-cyclic and codisk-cyclic weighted pseudo-shifts.Bull. Belg. Math. Soc. - Simon Stevin 25 (2018), 209-224. Zbl 06916056, MR 3819123, 10.36045/bbms/1530065010 |
| Reference:
|
[21] Zeana, Z. J.: Cyclic Phenomena of Operators on Hilbert Space: Ph.D. Thesis.University of Bagdad, Bagdad (2002). |
| . |
