On recurrent sets of operators

Resumo

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.

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Biografia do Autor

Mohamed Amouch, Chouaib Doukkali University

Department of Mathematics

Otmane Benchiheb, Université Chouaïb Doukkali – Faculté des Sciences d'El Jadida

Department of Mathematics

Referências

Amouch M, Benchiheb O (2022) Codiskcyclic sets of operators on complex topological vector spaces. Proyecciones (Antofagasta, On line) 41(6) 1439-1456.

Amouch M, Benchiheb O (2021) Some versions of supercyclicity for a set of operators. Filomat 35(5):1619-1627

Amouch M, Benchiheb O (2020) Diskcyclicity of sets of operators and applications. Acta Math Sin Eng Ser. 36(11):1203-1220.

Amouch M, Benchiheb O (2019) On cyclic sets of operators. Rendiconti del Circolo Matematico di Palermo Series 2. 68(3):521-529

Amouch M, Benchiheb O (2019) On linear dynamics of sets of operators. Turk J Math 43:402-411

Ansari M, Hedayatian K, Khani-robati, B (2018) On the density and transitivity of sets of operators. Turk J Math 42(1):181-189

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

Bayart F, Matheron E (2009) Dynamics of linear operators. New York, NY, USA, Cambridge University Press

Bonilla A, Grosse-Erdmann K. G, López-Martínez A, Peris A (2022) Frequently recurrent operators. Journal of Functional Analysis 283(12), 109713.

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

Costakis G, Manoussos A, Parissis I (2014) Recurrent linear operators. Complex Anal Oper Th 8:1601-1643

Costakis G, Parissis I (2012) Szemerédi’s theorem, frequent hypercyclicity and multiple recurrence. Math Scand 110: 251-272

Furstenberg H (1981) Recurrence in ergodic theory and combinatorial number theory. Princeton: Princeton University Press, M. B. Porter Lectures

Galán V.J, Martlínez-Gimenez F, Oprocha P, Peris A (2015) Product recurrence for weighted backward shifts. Appl. Math. Inf. Sci. 9: 2361-2365.

Grosse-Erdmann K.-G, Peris A (2011) Linear Chaos. (Universitext). Springer, London

Hilden HM, Wallen LJ (1994) Some cyclic and non-cyclic vectors of certain operators. Indiana Univ Math J 23:557-565

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

Publicado
2024-05-21
Seção
Artigos