Publication: Reducing subspaces for rank-one perturbations of normal operators
dc.affiliation.dpto | UC3M. Departamento de Matemáticas | es |
dc.affiliation.grupoinv | UC3M. Grupo de Investigación: Análisis Aplicado | es |
dc.contributor.author | Gallardo Gutiérrez, Eva A. | |
dc.contributor.author | González Doña, Francisco Javier | |
dc.contributor.funder | Ministerio de Ciencia e Innovación (España) | es |
dc.contributor.funder | Consejo Superior de Investigaciones Científicas (España) | es |
dc.contributor.funder | Agencia Estatal de Investigación (España) | es |
dc.date.accessioned | 2024-07-24T10:54:57Z | |
dc.date.available | 2024-07-24T10:54:57Z | |
dc.date.issued | 2023-08-01 | |
dc.description.abstract | We study the existence of reducing subspaces for rank-one perturbations of diagonal operators and, in general, of normal operators of uniform multiplicity one. As we will show, the spectral picture will play a significant role in order to prove the existence of reducing subspaces for rank-one perturbations of diagonal operators whenever they are not normal. In this regard, the most extreme case is provided when the spectrum of the rank-one perturbation of a diagonal operator T=D+u¿v (uniquely determined by such expression) is contained in a line, since in such a case T has a reducing subspace if and only if T is normal. Nevertheless, we will show that it is possible to exhibit non-normal operators T=D+u¿v with spectrum contained in a circle either having or lacking non-trivial reducing subspaces. Moreover, as far as the spectrum of T is contained in any compact subset of the complex plane, we provide a characterization of the reducing subspaces M of T such that the restriction T¿M is normal. In particular, such characterization allows us to exhibit rank-one perturbations of completely normal diagonal operators (in the sense of Wermer) lacking reducing subspaces. Furthermore, it determines completely the decomposition of the underlying Hilbert space in an orthogonal sum of reducing subspaces in the context of a classical theorem due to Behncke on essentially normal operators. | es |
dc.description.sponsorship | Both authors are partially supported by Plan Nacional I+D grant no. PID2019105979GB-I00, Spain, the Spanish Ministry of Science and Innovation, through the `Severo Ochoa Programme for Centres of Excellence in R&D' (SEV-20150554) and from the Spanish National Research Council, through the `Ayuda extraordinaria a Centros de Excelencia Severo Ochoa' (20205CEX001). The second author also acknowledges support of the Grant SEV-2015-0554-18-3 funded by: MCIN/AEI/10.13039/501100011033. | en |
dc.format.extent | 33 | |
dc.identifier.bibliographicCitation | Gallardo-Gutiérrez, E. A., & González-Doña, F. J. (2023). Reducing subspaces for rank-one perturbations of normal operators. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 153(4), 1391–1423. doi:10.1017/prm.2022.51 | en |
dc.identifier.doi | https://doi.org/10.1017/prm.2022.51 | |
dc.identifier.issn | 0308-2105 | |
dc.identifier.issn | 1473-7124 (eISSN) | |
dc.identifier.publicationfirstpage | 1391 | |
dc.identifier.publicationissue | 4 | |
dc.identifier.publicationlastpage | 1423 | |
dc.identifier.publicationtitle | Proceedings of the Royal Society of Edinburgh. Section A: Mathematics | en |
dc.identifier.publicationvolume | 153 | |
dc.identifier.uri | https://hdl.handle.net/10016/44213 | |
dc.identifier.uxxi | AR/0000033345 | |
dc.relation.projectID | Gobierno de España. PID2019-105979GB-I00 | es |
dc.relation.projectID | Consejo Superior de Investigaciones Científicas. 20205CEX001 | es |
dc.relation.projectID | Gobierno de España. SEV-2015-0554-18-3 | es |
dc.rights | © The Author(s), 2022 | en |
dc.rights | Published by Cambridge University Press on behalf of The Royal Society of Edinburgh. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. | en |
dc.rights.accessRights | open access | en |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en |
dc.subject.eciencia | Matemáticas | |
dc.subject.other | Reducing subspaces | en |
dc.subject.other | Rank-one perturbation of diagonal operators | en |
dc.subject.other | Rank-one perturbation of normal operators | en |
dc.title | Reducing subspaces for rank-one perturbations of normal operators | es |
dc.type | research article | en |
dc.type.hasVersion | VoR | en |
dspace.entity.type | Publication | en |
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