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dc.contributor.author | López-Martínez, Antoni![]() |
es_ES |
dc.date.accessioned | 2024-05-16T18:08:45Z | |
dc.date.available | 2024-05-16T18:08:45Z | |
dc.date.issued | 2024-01-20 | es_ES |
dc.identifier.issn | 1073-7928 | es_ES |
dc.identifier.uri | http://hdl.handle.net/10251/204213 | |
dc.description.abstract | [EN] We study the spaceability of the set of recurrent vectors $\text{Rec}(T)$ for an operator $T:X\longrightarrow X$ on a Banach space $X$. In particular, we find sufficient conditions for a quasi-rigid operator to have a recurrent subspace; when $X$ is a complex Banach space, we show that having a recurrent subspace is equivalent to the fact that the essential spectrum of the operator intersects the closed unit disk, and we extend the previous result to the real case. As a consequence, we obtain that a weakly-mixing operator on a real or complex separable Banach space has a hypercyclic subspace if and only if it has a recurrent subspace. The results exposed exhibit a symmetry between the hypercyclic and recurrent spaceability theories showing that, at least for the spaceable property, hypercyclicity and recurrence can be treated as equals. | es_ES |
dc.description.sponsorship | This work was partially supported by the Spanish Ministerio de Ciencia, Innovacion y Universidades [FPU2019/04094]; and also partially supported by MCIN/AEI/10.13039/501100011033/FEDER, UE [Projects PID2019-105011GB-I00 and PID2022-139449NB-I00]. | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | Oxford University Press | es_ES |
dc.relation.ispartof | International Mathematics Research Notices | es_ES |
dc.rights | Reserva de todos los derechos | es_ES |
dc.title | Recurrent Subspaces in Banach Spaces | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.1093/imrn/rnad321 | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-105011GB-I00/ES/DINAMICA DE OPERADORES/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-139449NB-I00/ES/DINAMICA DE OPERADORES Y ECUACIONES DE EVOLUCION/ | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/MCIU//FPU2019%2F04094/ | es_ES |
dc.rights.accessRights | Embargado | es_ES |
dc.date.embargoEndDate | 2025-01-20 | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada | es_ES |
dc.description.bibliographicCitation | López-Martínez, A. (2024). Recurrent Subspaces in Banach Spaces. International Mathematics Research Notices. 1-21. https://doi.org/10.1093/imrn/rnad321 | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | https://doi.org/10.1093/imrn/rnad321 | es_ES |
dc.description.upvformatpinicio | 1 | es_ES |
dc.description.upvformatpfin | 21 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.relation.pasarela | S\513736 | es_ES |
dc.contributor.funder | Agencia Estatal de Investigación | es_ES |
dc.contributor.funder | European Regional Development Fund | es_ES |
dc.contributor.funder | Ministerio de Ciencia, Innovación y Universidades | es_ES |