On recurrent sets of operators
DOI :
https://doi.org/10.5269/bspm.66691Résumé
An operator $T$ acting on a Banach space $X$ is said to be recurrent if for each $U$; a nonempty open subset of $X$, there exists $n\in\mathbb{N}$ such that $T^n(U)\cap U\neq\emptyset.$ In the present work, we generalize this notion from a single operator to a set $\Gamma$ of operators. As application, we study the recurrence of $C$-regularized group of operators.Références
1. Amouch M, Benchiheb O (2022) Codiskcyclic sets of operators on complex topological vector spaces. Proyecciones (Antofagasta, On line) 41(6) 1439-1456.
2. Amouch M, Benchiheb O (2021) Some versions of supercyclicity for a set of operators. Filomat 35(5):1619-1627
3. Amouch M, Benchiheb O (2020) Diskcyclicity of sets of operators and applications. Acta Math Sin Eng Ser. 36(11):1203-1220.
4. Amouch M, Benchiheb O (2019) On cyclic sets of operators. Rendiconti del Circolo Matematico di Palermo Series 2. 68(3):521-529
5. Amouch M, Benchiheb O (2019) On linear dynamics of sets of operators. Turk J Math 43:402-411
6. Ansari M, Hedayatian K, Khani-robati, B (2018) On the density and transitivity of sets of operators. Turk J Math 42(1):181-189
7. Ansari M, Hedayatian K, Khani Robati B, Moradi A (2018) A note on topological and strict transitivity. Iran J Sci Technol Trans Sci 42(1):59-64
8. Bayart F, Matheron E (2009) Dynamics of linear operators. New York, NY, USA, Cambridge University Press
9. Bonilla A, Grosse-Erdmann K. G, López-Martínez A, Peris A (2022) Frequently recurrent operators. Journal of Functional Analysis 283(12), 109713.
10. Conejero JA, Kostic M, Miana PJ, Murillo-Arcila M (2016) Distributionally chaotic families of operators on Frechet spaces. Commun Pure Appl Anal 15(5):1915-1939
11. Costakis G, Manoussos A, Parissis I (2014) Recurrent linear operators. Complex Anal Oper Th 8:1601-1643
12. Costakis G, Parissis I (2012) Szemerédi’s theorem, frequent hypercyclicity and multiple recurrence. Math Scand 110: 251-272
13. Furstenberg H (1981) Recurrence in ergodic theory and combinatorial number theory. Princeton: Princeton University Press, M. B. Porter Lectures
14. Galán V.J, Martlínez-Gimenez F, Oprocha P, Peris A (2015) Product recurrence for weighted backward shifts. Appl. Math. Inf. Sci. 9: 2361-2365.
15. Grosse-Erdmann K.-G, Peris A (2011) Linear Chaos. (Universitext). Springer, London
16. Hilden HM, Wallen LJ (1994) Some cyclic and non-cyclic vectors of certain operators. Indiana Univ Math J 23:557-565
17. Karim N, Benchiheb O, Amouch M (2022) Recurrence of multiples of composition operators on weighted Dirichlet spaces. Adv Oper Theory 7(23) https://doi.org/10.1007/s43036-022-00186-1
2. Amouch M, Benchiheb O (2021) Some versions of supercyclicity for a set of operators. Filomat 35(5):1619-1627
3. Amouch M, Benchiheb O (2020) Diskcyclicity of sets of operators and applications. Acta Math Sin Eng Ser. 36(11):1203-1220.
4. Amouch M, Benchiheb O (2019) On cyclic sets of operators. Rendiconti del Circolo Matematico di Palermo Series 2. 68(3):521-529
5. Amouch M, Benchiheb O (2019) On linear dynamics of sets of operators. Turk J Math 43:402-411
6. Ansari M, Hedayatian K, Khani-robati, B (2018) On the density and transitivity of sets of operators. Turk J Math 42(1):181-189
7. Ansari M, Hedayatian K, Khani Robati B, Moradi A (2018) A note on topological and strict transitivity. Iran J Sci Technol Trans Sci 42(1):59-64
8. Bayart F, Matheron E (2009) Dynamics of linear operators. New York, NY, USA, Cambridge University Press
9. Bonilla A, Grosse-Erdmann K. G, López-Martínez A, Peris A (2022) Frequently recurrent operators. Journal of Functional Analysis 283(12), 109713.
10. Conejero JA, Kostic M, Miana PJ, Murillo-Arcila M (2016) Distributionally chaotic families of operators on Frechet spaces. Commun Pure Appl Anal 15(5):1915-1939
11. Costakis G, Manoussos A, Parissis I (2014) Recurrent linear operators. Complex Anal Oper Th 8:1601-1643
12. Costakis G, Parissis I (2012) Szemerédi’s theorem, frequent hypercyclicity and multiple recurrence. Math Scand 110: 251-272
13. Furstenberg H (1981) Recurrence in ergodic theory and combinatorial number theory. Princeton: Princeton University Press, M. B. Porter Lectures
14. Galán V.J, Martlínez-Gimenez F, Oprocha P, Peris A (2015) Product recurrence for weighted backward shifts. Appl. Math. Inf. Sci. 9: 2361-2365.
15. Grosse-Erdmann K.-G, Peris A (2011) Linear Chaos. (Universitext). Springer, London
16. Hilden HM, Wallen LJ (1994) Some cyclic and non-cyclic vectors of certain operators. Indiana Univ Math J 23:557-565
17. Karim N, Benchiheb O, Amouch M (2022) Recurrence of multiples of composition operators on weighted Dirichlet spaces. Adv Oper Theory 7(23) https://doi.org/10.1007/s43036-022-00186-1
Téléchargements
Publié
2024-05-21
Numéro
Rubrique
Research Articles
Licence
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
