Simultaneous zero inclusion property for spatial numerical ranges
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10071/13071 |
Resumo: | For a finite dimensional complex normed space X, we say that it has the simultaneous zero inclusion property if an invertible linear operator S on X has zero in its spatial numerical range if and only if zero is in the spatial numerical range of the inverse S-1, as well. We show that beside Hilbert spaces there are some other normed spaces with this property. On the other hand, space l(1) (n) does not have this property. Since not every normed space has the simultaneous zero inclusion property, we explore the class of invertible operators at which this property holds. In the end, we consider a property which is stronger than the simultaneous zero inclusion property and is related to the question when it is possible, for every invertible operator S, to control the distance of 0 to the spatial numerical range of S-1 by the distance of 0 to the spatial numerical range of S. |
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Simultaneous zero inclusion property for spatial numerical rangesSpatial numerical rangeFor a finite dimensional complex normed space X, we say that it has the simultaneous zero inclusion property if an invertible linear operator S on X has zero in its spatial numerical range if and only if zero is in the spatial numerical range of the inverse S-1, as well. We show that beside Hilbert spaces there are some other normed spaces with this property. On the other hand, space l(1) (n) does not have this property. Since not every normed space has the simultaneous zero inclusion property, we explore the class of invertible operators at which this property holds. In the end, we consider a property which is stronger than the simultaneous zero inclusion property and is related to the question when it is possible, for every invertible operator S, to control the distance of 0 to the spatial numerical range of S-1 by the distance of 0 to the spatial numerical range of S.Academic Press/Elsevier2017-04-20T14:55:51Z2017-01-01T00:00:00Z20172019-03-21T17:44:30Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10071/13071eng0022-247X10.1016/j.jmaa.2017.01.001Bracic, J.Diogo, C.info:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-09T17:58:47Zoai:repositorio.iscte-iul.pt:10071/13071Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:30:40.155237Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Simultaneous zero inclusion property for spatial numerical ranges |
title |
Simultaneous zero inclusion property for spatial numerical ranges |
spellingShingle |
Simultaneous zero inclusion property for spatial numerical ranges Bracic, J. Spatial numerical range |
title_short |
Simultaneous zero inclusion property for spatial numerical ranges |
title_full |
Simultaneous zero inclusion property for spatial numerical ranges |
title_fullStr |
Simultaneous zero inclusion property for spatial numerical ranges |
title_full_unstemmed |
Simultaneous zero inclusion property for spatial numerical ranges |
title_sort |
Simultaneous zero inclusion property for spatial numerical ranges |
author |
Bracic, J. |
author_facet |
Bracic, J. Diogo, C. |
author_role |
author |
author2 |
Diogo, C. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Bracic, J. Diogo, C. |
dc.subject.por.fl_str_mv |
Spatial numerical range |
topic |
Spatial numerical range |
description |
For a finite dimensional complex normed space X, we say that it has the simultaneous zero inclusion property if an invertible linear operator S on X has zero in its spatial numerical range if and only if zero is in the spatial numerical range of the inverse S-1, as well. We show that beside Hilbert spaces there are some other normed spaces with this property. On the other hand, space l(1) (n) does not have this property. Since not every normed space has the simultaneous zero inclusion property, we explore the class of invertible operators at which this property holds. In the end, we consider a property which is stronger than the simultaneous zero inclusion property and is related to the question when it is possible, for every invertible operator S, to control the distance of 0 to the spatial numerical range of S-1 by the distance of 0 to the spatial numerical range of S. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-04-20T14:55:51Z 2017-01-01T00:00:00Z 2017 2019-03-21T17:44:30Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10071/13071 |
url |
http://hdl.handle.net/10071/13071 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0022-247X 10.1016/j.jmaa.2017.01.001 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/embargoedAccess |
eu_rights_str_mv |
embargoedAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Academic Press/Elsevier |
publisher.none.fl_str_mv |
Academic Press/Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799134868635910144 |