Band projections and order idempotents in Banach lattice algebras

Motivated by recent work about band projections on spaces of regular operators over a Banach lattice, given a Banach lattice algebra A, we will say an element a ∈ A + is a band projection if the multiplication operator LaRa ∈Lr(A)is a band projection. Our aim in this note is to explore the relations...

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Detalles Bibliográficos
Autor: Muñoz Lahoz, David
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/716555
Acceso en línea:http://hdl.handle.net/10486/716555
https://dx.doi.org/10.1016/j.jmaa.2024.129045
Access Level:acceso abierto
Palabra clave:Banach Lattice Algebra
Band Projection
Order Idempotent
Regular Operator
Matemáticas
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spelling Band projections and order idempotents in Banach lattice algebrasMuñoz Lahoz, DavidBanach Lattice AlgebraBand ProjectionOrder IdempotentRegular OperatorMatemáticasMotivated by recent work about band projections on spaces of regular operators over a Banach lattice, given a Banach lattice algebra A, we will say an element a ∈ A + is a band projection if the multiplication operator LaRa ∈Lr(A)is a band projection. Our aim in this note is to explore the relations between this and the notion of order idempotent (those elements a in a Banach lattice algebra A with identity e such that 0 ≤ a ≤ e and a2 = a). We also revisit the properties of the ideal generated by the identity on a Banach lattice algebra, motivated by those of the centre of a Banach latticeResearch partially supported by an FPI–UAM 2023 contract funded by Universidad Autónoma de MadridElsevierDepartamento de MatemáticasFacultad de Ciencias20252025-03-15research articlehttp://purl.org/coar/resource_type/c_2df8fbb1VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/716555https://dx.doi.org/10.1016/j.jmaa.2024.129045reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/7165552026-06-23T12:46:27Z
dc.title.none.fl_str_mv Band projections and order idempotents in Banach lattice algebras
title Band projections and order idempotents in Banach lattice algebras
spellingShingle Band projections and order idempotents in Banach lattice algebras
Muñoz Lahoz, David
Banach Lattice Algebra
Band Projection
Order Idempotent
Regular Operator
Matemáticas
title_short Band projections and order idempotents in Banach lattice algebras
title_full Band projections and order idempotents in Banach lattice algebras
title_fullStr Band projections and order idempotents in Banach lattice algebras
title_full_unstemmed Band projections and order idempotents in Banach lattice algebras
title_sort Band projections and order idempotents in Banach lattice algebras
dc.creator.none.fl_str_mv Muñoz Lahoz, David
author Muñoz Lahoz, David
author_facet Muñoz Lahoz, David
author_role author
dc.contributor.none.fl_str_mv Departamento de Matemáticas
Facultad de Ciencias
dc.subject.none.fl_str_mv Banach Lattice Algebra
Band Projection
Order Idempotent
Regular Operator
Matemáticas
topic Banach Lattice Algebra
Band Projection
Order Idempotent
Regular Operator
Matemáticas
description Motivated by recent work about band projections on spaces of regular operators over a Banach lattice, given a Banach lattice algebra A, we will say an element a ∈ A + is a band projection if the multiplication operator LaRa ∈Lr(A)is a band projection. Our aim in this note is to explore the relations between this and the notion of order idempotent (those elements a in a Banach lattice algebra A with identity e such that 0 ≤ a ≤ e and a2 = a). We also revisit the properties of the ideal generated by the identity on a Banach lattice algebra, motivated by those of the centre of a Banach lattice
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-03-15
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10486/716555
https://dx.doi.org/10.1016/j.jmaa.2024.129045
url http://hdl.handle.net/10486/716555
https://dx.doi.org/10.1016/j.jmaa.2024.129045
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
collection Biblos-e Archivo. Repositorio Institucional de la UAM
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