[en] Chan and Seceleanu have shown that if a weighted shift operator on (Formula presented), (Formula presented), admits an orbit with a non-zero limit point then it is hypercyclic. We present a new proof of this result that allows to extend it to very general sequence spaces. In a similar vein, we show that, in many sequence spaces, a weighted shift with a non-zero weakly sequentially recurrent vector has a dense set of such vectors, but an example on (Formula presented) shows that such an operator is not necessarily hypercyclic. On the other hand, we obtain that weakly sequentially hypercyclic weighted shifts are hypercyclic. Chan and Seceleanu have, moreover, shown that if an adjoint multiplication operator on a Bergman space admits an orbit with a non-zero limit point then it is hypercyclic. We extend this result to very general spaces of analytic functions, including the Hardy spaces.
Research center :
CREMMI - Modélisation mathématique et informatique
Disciplines :
Mathematics
Author, co-author :
Bonilla, Antonio ✱; Departamento de Análisis Matemático, Instituto de Matemáticas y Aplicaciones (IMAULL), Universidad de La Laguna, La Laguna, Spain
Cardeccia, Rodrigo ✱; Departamento de Matemática, Instituto Balseiro, Universidad Nacional de Cuyo, C.N.E.A. and CONICET, San Carlos de Bariloche, Argentina
Grosse-Erdmann, Karl ✱; Université de Mons - UMONS > Faculté des Sciences > Service d'Analyse fonctionnelle
Muro, Santiago ✱; FCEIA, Universidad Nacional de Rosario and CIFASIS, CONICET, Rosario, Argentina
✱ These authors have contributed equally to this work.
Language :
English
Title :
Zero-one law of orbital limit points for weighted shifts
This publication is part of the project PID2022-139449NB-I00, funded by MCIN/AEI/10.13039/501100011033/FEDER, UE; the third author was supported by the Fonds de la Recherche Scientifique - FNRS under Grant n CDR J.0078.21; the second and fourth authors were supported by PICT 2018-4250 and CONICET.
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