A note on the essential numerical range of block diagonal operators

Detalhes bibliográficos
Autor(a) principal: Carvalho, L.
Data de Publicação: 2023
Outros Autores: Diogo, C., Mendes, S., Soares, H.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10071/30724
Resumo: In this note we characterize the essential numerical range of a block diagonal operator T = ⊕i T_i in terms of the numerical ranges {W (T_i )}i of its components. Specifically, the essential numerical range of T is the convex hull of the limit superior of {W (Ti )}i . This characterization can be simplified further. In fact, we prove the existence of a decomposition of T for which the convex hull is not required.
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spelling A note on the essential numerical range of block diagonal operatorsBlock diagonal operatorEssential numerical rangeIn this note we characterize the essential numerical range of a block diagonal operator T = ⊕i T_i in terms of the numerical ranges {W (T_i )}i of its components. Specifically, the essential numerical range of T is the convex hull of the limit superior of {W (Ti )}i . This characterization can be simplified further. In fact, we prove the existence of a decomposition of T for which the convex hull is not required.Walter de Gruyter GmbH2024-11-29T00:00:00Z2023-01-01T00:00:00Z20232024-01-31T11:21:18Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10071/30724eng0933-774110.1515/forum-2023-0166Carvalho, L.Diogo, C.Mendes, S.Soares, H.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:RCAAP2024-02-04T01:19:51Zoai:repositorio.iscte-iul.pt:10071/30724Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:08:02.485495Repositório 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 A note on the essential numerical range of block diagonal operators
title A note on the essential numerical range of block diagonal operators
spellingShingle A note on the essential numerical range of block diagonal operators
Carvalho, L.
Block diagonal operator
Essential numerical range
title_short A note on the essential numerical range of block diagonal operators
title_full A note on the essential numerical range of block diagonal operators
title_fullStr A note on the essential numerical range of block diagonal operators
title_full_unstemmed A note on the essential numerical range of block diagonal operators
title_sort A note on the essential numerical range of block diagonal operators
author Carvalho, L.
author_facet Carvalho, L.
Diogo, C.
Mendes, S.
Soares, H.
author_role author
author2 Diogo, C.
Mendes, S.
Soares, H.
author2_role author
author
author
dc.contributor.author.fl_str_mv Carvalho, L.
Diogo, C.
Mendes, S.
Soares, H.
dc.subject.por.fl_str_mv Block diagonal operator
Essential numerical range
topic Block diagonal operator
Essential numerical range
description In this note we characterize the essential numerical range of a block diagonal operator T = ⊕i T_i in terms of the numerical ranges {W (T_i )}i of its components. Specifically, the essential numerical range of T is the convex hull of the limit superior of {W (Ti )}i . This characterization can be simplified further. In fact, we prove the existence of a decomposition of T for which the convex hull is not required.
publishDate 2023
dc.date.none.fl_str_mv 2023-01-01T00:00:00Z
2023
2024-11-29T00:00:00Z
2024-01-31T11:21:18Z
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/10071/30724
url http://hdl.handle.net/10071/30724
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0933-7741
10.1515/forum-2023-0166
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 Walter de Gruyter GmbH
publisher.none.fl_str_mv Walter de Gruyter GmbH
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
repository.mail.fl_str_mv
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