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dc.contributor.author
Dantas, Sheldon
dc.contributor.author
Kim, Sun Kwang
dc.contributor.author
Lee, Han Ju
dc.contributor.author
Mazzitelli, Martin Diego
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dc.date.available
2024-01-09T11:17:44Z
dc.date.issued
2023-02
dc.identifier.citation
Dantas, Sheldon; Kim, Sun Kwang; Lee, Han Ju; Mazzitelli, Martin Diego; On various types of density of numerical radius attaining operators; Taylor & Francis Ltd; Linear And Multilinear Algebra; 2-2023; 1-18
dc.identifier.issn
0308-1087
dc.identifier.uri
http://hdl.handle.net/11336/222919
dc.description.abstract
In this paper, we are interested in studying Bishop–Phelps–Bollobás type properties related to the denseness of the operators which attain their numerical radius. We prove that every Banach space with a micro-transitive norm and the second numerical index strictly positive satisfies the Bishop–Phelps–Bollobás point property, and we see that the one-dimensional space is the only one with both the numerical index 1 and the Bishop–Phelps–Bollobás point property. We also consider two weaker properties L (Formula presented.) -nu and L (Formula presented.) -nu, the local versions of Bishop–Phelps–Bollobás point and operator properties respectively, where the η which appears in their definition does not depend just on (Formula presented.) but also on a state (Formula presented.) or on a numerical radius one operator T. We address the relation between the L (Formula presented.) -nu and the strong subdifferentiability of the norm of the space X. We show that finite dimensional spaces and (Formula presented.) are examples of Banach spaces satisfying the L (Formula presented.) -nu, and we exhibit an example of a Banach space with a strongly subdifferentiable norm failing it. We finish the paper by showing that finite dimensional spaces satisfy the L (Formula presented.) -nu and that, if X has a strictly positive numerical index and has the approximation property, this property is equivalent to finite dimensionality.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Taylor & Francis Ltd
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dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
46B20
dc.subject
BANACH SPACE
dc.subject
BISHOP-PHELPS-BOLLOBÁS PROPERTY
dc.subject
NUMERICAL RADIUS ATTAINING OPERATORS
dc.subject
PRIMARY: 46B04
dc.subject
SECONDARY: 46B07
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
On various types of density of numerical radius attaining operators
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2024-01-08T14:21:06Z
dc.journal.pagination
1-18
dc.journal.pais
Reino Unido
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dc.journal.ciudad
Londres
dc.description.fil
Fil: Dantas, Sheldon. Universidad de Valencia; España
dc.description.fil
Fil: Kim, Sun Kwang. Chungbuk National University; Corea del Norte
dc.description.fil
Fil: Lee, Han Ju. Dongguk University; Corea del Norte
dc.description.fil
Fil: Mazzitelli, Martin Diego. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro | Universidad Nacional de Cuyo. Instituto Balseiro. Archivo Histórico del Centro Atómico Bariloche e Instituto Balseiro; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina
dc.journal.title
Linear And Multilinear Algebra
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.tandfonline.com/doi/full/10.1080/03081087.2023.2176413
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1080/03081087.2023.2176413
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