Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 260
A note on multiply recurrent operators
Fatima-Ezzahra Sadek, Mohamed Amouch
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 29, 2022
March 03, 2229
April 15, 2229

Abstract: The notion of recurrence has been introduced first in 1890 by Poincaré with the Poincaré recurrence theorem (see [6]) and generalized after that by Furstenberg in 1976 to Multiple recurrence theorem (see [5]). These two notions have been studied structurally in the linear dynamic by G. Costakis et al. in [4] and Cardeccia et al. in [3]. In this communication, we study the notion of multiply recurrent vector for an operator on a Banach space X. We give a characterization of topologically multiply recurrent for an operator on X by means of the set of all multiply recurrent vectors. We also ...