Orbits of the backward shifts with limit points

We show that the bilateral backward shift on ℓp(Z,ω) that has a projective orbit with a non-zero limit point is supercyclic. This phenomenon holds also for Γ-supercyclicity, which extends a result obtained for the first time by Chan and Seceleanu. Moreover, we show that if K is a compact subset of ℓ...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications Vol. 537; no. 2; p. 128293
Main Authors: Abakumov, Evgeny, Abbar, Arafat
Format: Journal Article
Language:English
Published: Elsevier Inc 15.09.2024
Subjects:
Backward shift
Hypercyclicity
Orbital limit points
Recurrence
Supercyclicity
Translation semigroup
Backward shift
Recurrence
Supercyclicity
Hypercyclicity
Translation semigroup
Orbital limit points
ISSN:0022-247X
Online Access:Get full text
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Summary:We show that the bilateral backward shift on ℓp(Z,ω) that has a projective orbit with a non-zero limit point is supercyclic. This phenomenon holds also for Γ-supercyclicity, which extends a result obtained for the first time by Chan and Seceleanu. Moreover, we show that if K is a compact subset of ℓp(N,ω) such that its orbit under the unilateral backward shift B on ℓp(N,ω) has a non-zero weak limit point, then B is hypercyclic. Similar results for translation semigroups on weighted Lebesgue spaces are obtained.
ISSN:0022-247X
DOI:10.1016/j.jmaa.2024.128293