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Papers published in the English version of the journal

Weakly Sequentially Recurrent Shifts Operators

M. Amouch^a, A. Bachir^b, O. Benchiheb^a, S. Mecheri<sup>c

a</sup> Department of Mathematics, Faculty of Science, Chouaib Doukkali University
^b Department of Mathematics, Faculty of Science, King Khalid University
^c Department of Mathematics, Faculty of Science and Informatics, Mohamed El Bachir El Ibrahimi University

Abstract: This paper studies the weakly sequentially recurrence property of shifts operators. In the case of $\ell^p(\mathbb{N})$, $1\leq p<\infty$, we show that the weak recurrence, recurrence, hypercyclicity, and weak hypercyclicity are equivalent. In the case of $\ell^\infty(\mathbb{N})$ (resp. $\ell^\infty(\mathbb{Z})$), we prove that the unilateral backward (resp. bilateral backward) can never be weakly sequentially recurrent.

Keywords: hypercyclicity, weak hypercyclicity, recurrence, weak recurrence, shifts operators.

MSC: Primary 47A16, 37B20; Secondary 46E50, 46T25

Received: 19.05.2023
Revised: 31.07.2023

Language: English

 English version: Mathematical Notes, 2023, 114:5, 668–674

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