Fast orbital convergence reveals more hypercyclic vectors

[EN] Let X be an infinite dimensional separable Banach space, T : X → X be a hypercyclic operator, and x ∈ X be a (frequently) hypercyclic vector of T. We show that if the terms from the T-orbit of x converge to a vector y sufficiently fast, then y is also a hypercyclic vector of T. As a corollary,...

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Detalles Bibliográficos
Autor: Moothathu, TKS Moothathu
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/227675
Acceso en línea:https://riunet.upv.es/handle/10251/227675
Access Level:acceso abierto
Palabra clave:Banach space
Hypercyclic operator
Orbital speed
Frequent hypercyclicity
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repository_id_str
spelling Fast orbital convergence reveals more hypercyclic vectorsMoothathu, TKS MoothathuBanach spaceHypercyclic operatorOrbital speedFrequent hypercyclicity[EN] Let X be an infinite dimensional separable Banach space, T : X → X be a hypercyclic operator, and x ∈ X be a (frequently) hypercyclic vector of T. We show that if the terms from the T-orbit of x converge to a vector y sufficiently fast, then y is also a hypercyclic vector of T. As a corollary, we deduce that if T is a frequently hypercyclic operator with spectral radius r(T) = 1, then lim_{n\to \infty} ∥Tnx∥^{1/n} = 1 for every frequently hypercyclic vector x of T. Some related observations are also made.Universitat Politècnica de ValènciaRepositorio Institucional de la Universitat Politècnica de València Riunet20252025-10-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdftext/htmlhttps://riunet.upv.es/handle/10251/227675reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Compartir igual (by-nc-sa) http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2276752026-06-13T07:49:27Z
dc.title.none.fl_str_mv Fast orbital convergence reveals more hypercyclic vectors
title Fast orbital convergence reveals more hypercyclic vectors
spellingShingle Fast orbital convergence reveals more hypercyclic vectors
Moothathu, TKS Moothathu
Banach space
Hypercyclic operator
Orbital speed
Frequent hypercyclicity
title_short Fast orbital convergence reveals more hypercyclic vectors
title_full Fast orbital convergence reveals more hypercyclic vectors
title_fullStr Fast orbital convergence reveals more hypercyclic vectors
title_full_unstemmed Fast orbital convergence reveals more hypercyclic vectors
title_sort Fast orbital convergence reveals more hypercyclic vectors
dc.creator.none.fl_str_mv Moothathu, TKS Moothathu
author Moothathu, TKS Moothathu
author_facet Moothathu, TKS Moothathu
author_role author
dc.contributor.none.fl_str_mv Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Banach space
Hypercyclic operator
Orbital speed
Frequent hypercyclicity
topic Banach space
Hypercyclic operator
Orbital speed
Frequent hypercyclicity
description [EN] Let X be an infinite dimensional separable Banach space, T : X → X be a hypercyclic operator, and x ∈ X be a (frequently) hypercyclic vector of T. We show that if the terms from the T-orbit of x converge to a vector y sufficiently fast, then y is also a hypercyclic vector of T. As a corollary, we deduce that if T is a frequently hypercyclic operator with spectral radius r(T) = 1, then lim_{n\to \infty} ∥Tnx∥^{1/n} = 1 for every frequently hypercyclic vector x of T. Some related observations are also made.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-10-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/227675
url https://riunet.upv.es/handle/10251/227675
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Compartir igual (by-nc-sa)
http://creativecommons.org/licenses/by-nc-sa/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Compartir igual (by-nc-sa)
http://creativecommons.org/licenses/by-nc-sa/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
text/html
dc.publisher.none.fl_str_mv Universitat Politècnica de València
publisher.none.fl_str_mv Universitat Politècnica de València
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.81155

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