Hypercyclic subspaces in Fréchet spaces

In this note, we show that every infinite-dimensional separable Fr´echet space admitting a continuous norm supports an operator for which there is an infinite-dimensional closed subspace consisting, except for zero, of hypercyclic vectors. The family of such operators is even dense in the space of b...

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Detalles Bibliográficos
Autor: Bernal González, Luis
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2006
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/87517
Acceso en línea:https://hdl.handle.net/11441/87517
https://doi.org/10.1090/S0002-9939-05-08242-0
Access Level:acceso abierto
Palabra clave:Hypercyclic operator
Hypercyclic sequence
Hypercyclic subspace
Backward shift
Fréchet space
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spelling Hypercyclic subspaces in Fréchet spacesBernal González, LuisHypercyclic operatorHypercyclic sequenceHypercyclic subspaceBackward shiftFréchet spaceIn this note, we show that every infinite-dimensional separable Fr´echet space admitting a continuous norm supports an operator for which there is an infinite-dimensional closed subspace consisting, except for zero, of hypercyclic vectors. The family of such operators is even dense in the space of bounded operators when endowed with the strong operator topology. This completes earlier work of several authors.Plan Andaluz de Investigación (Junta de Andalucía)Dirección General de Enseñanza Superior (DGES). EspañaAmerican Mathematical SocietyAnálisis MatemáticoFQM127: Análisis Funcional no Lineal2006info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/87517https://doi.org/10.1090/S0002-9939-05-08242-0reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésProceedings of the American Mathematical Society, 134 (7), 1955-1961.FQM-127BFM2003-03893-C02-01http://www.ams.org/journals/proc/2006-134-07/S0002-9939-05-08242-0/S0002-9939-05-08242-0.pdfinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/875172026-06-17T12:51:07Z
dc.title.none.fl_str_mv Hypercyclic subspaces in Fréchet spaces
title Hypercyclic subspaces in Fréchet spaces
spellingShingle Hypercyclic subspaces in Fréchet spaces
Bernal González, Luis
Hypercyclic operator
Hypercyclic sequence
Hypercyclic subspace
Backward shift
Fréchet space
title_short Hypercyclic subspaces in Fréchet spaces
title_full Hypercyclic subspaces in Fréchet spaces
title_fullStr Hypercyclic subspaces in Fréchet spaces
title_full_unstemmed Hypercyclic subspaces in Fréchet spaces
title_sort Hypercyclic subspaces in Fréchet spaces
dc.creator.none.fl_str_mv Bernal González, Luis
author Bernal González, Luis
author_facet Bernal González, Luis
author_role author
dc.contributor.none.fl_str_mv Análisis Matemático
FQM127: Análisis Funcional no Lineal
dc.subject.none.fl_str_mv Hypercyclic operator
Hypercyclic sequence
Hypercyclic subspace
Backward shift
Fréchet space
topic Hypercyclic operator
Hypercyclic sequence
Hypercyclic subspace
Backward shift
Fréchet space
description In this note, we show that every infinite-dimensional separable Fr´echet space admitting a continuous norm supports an operator for which there is an infinite-dimensional closed subspace consisting, except for zero, of hypercyclic vectors. The family of such operators is even dense in the space of bounded operators when endowed with the strong operator topology. This completes earlier work of several authors.
publishDate 2006
dc.date.none.fl_str_mv 2006
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/87517
https://doi.org/10.1090/S0002-9939-05-08242-0
url https://hdl.handle.net/11441/87517
https://doi.org/10.1090/S0002-9939-05-08242-0
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Proceedings of the American Mathematical Society, 134 (7), 1955-1961.
FQM-127
BFM2003-03893-C02-01
http://www.ams.org/journals/proc/2006-134-07/S0002-9939-05-08242-0/S0002-9939-05-08242-0.pdf
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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