BANACH LATTICE AM-ALGEBRAS

An analogue of Kakutani’s representation theorem for Banach lattice algebras is provided. We characterize Banach lattice algebras that embed as a closed sublattice-algebra of C(K) precisely as those with a positive approximate identity (eγ) such that x∗(eγ) → ⃦x∗⃦ for every positive functional x∗. W...

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Detalles Bibliográficos
Autores: Muñoz-Lahoz, D., Tradacete, P.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2025
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/420831
Acceso en línea:http://hdl.handle.net/10261/420831
https://www.scopus.com/inward/record.uri?eid=2-s2.0-105006528300&doi=10.1090%2Fproc%2F17173&partnerID=40&md5=d00c076d1ad0bee679945ba21887a78b
Access Level:acceso abierto
Palabra clave:AM-space
Banach lattice algebra
spaces of continuous functions
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spelling BANACH LATTICE AM-ALGEBRASMuñoz-Lahoz, D.Tradacete, P.AM-spaceBanach lattice algebraspaces of continuous functionsAn analogue of Kakutani’s representation theorem for Banach lattice algebras is provided. We characterize Banach lattice algebras that embed as a closed sublattice-algebra of C(K) precisely as those with a positive approximate identity (eγ) such that x∗(eγ) → ⃦x∗⃦ for every positive functional x∗. We also show that every Banach lattice algebra with identity other than C(K) admits different product operations which are compatible with the order and the algebraic identity. This complements the classical result, due to Martignon, that on C(K) spaces pointwise multiplication is the unique compatible product. © 2025 American Mathematical Society.Research supported by grants PID2020-116398GB-I00 and CEX2019-000904-S funded by MICIU/AEI/10.13039/501100011033. Research of D. Mu˜noz-Lahoz supported by an FPI UAM2023contract funded by Universidad Aut´onoma de Madrid. Research of P. Tradacete also supported by a 2022 Leonardo Grant for Researchers and Cultural Creators, BBVA Foundation.Peer reviewedAmerican Mathematical SocietyMinisterio de Ciencia e Innovación (España)Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202620262025info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Preprintinfo:eu-repo/semantics/submittedVersionhttp://hdl.handle.net/10261/420831https://www.scopus.com/inward/record.uri?eid=2-s2.0-105006528300&doi=10.1090%2Fproc%2F17173&partnerID=40&md5=d00c076d1ad0bee679945ba21887a78breponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)InglésProceedings of the American Mathematical SocietySíinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/4208312026-05-22T06:33:51Z
dc.title.none.fl_str_mv BANACH LATTICE AM-ALGEBRAS
title BANACH LATTICE AM-ALGEBRAS
spellingShingle BANACH LATTICE AM-ALGEBRAS
Muñoz-Lahoz, D.
AM-space
Banach lattice algebra
spaces of continuous functions
title_short BANACH LATTICE AM-ALGEBRAS
title_full BANACH LATTICE AM-ALGEBRAS
title_fullStr BANACH LATTICE AM-ALGEBRAS
title_full_unstemmed BANACH LATTICE AM-ALGEBRAS
title_sort BANACH LATTICE AM-ALGEBRAS
dc.creator.none.fl_str_mv Muñoz-Lahoz, D.
Tradacete, P.
author Muñoz-Lahoz, D.
author_facet Muñoz-Lahoz, D.
Tradacete, P.
author_role author
author2 Tradacete, P.
author2_role author
dc.contributor.none.fl_str_mv Ministerio de Ciencia e Innovación (España)
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv AM-space
Banach lattice algebra
spaces of continuous functions
topic AM-space
Banach lattice algebra
spaces of continuous functions
description An analogue of Kakutani’s representation theorem for Banach lattice algebras is provided. We characterize Banach lattice algebras that embed as a closed sublattice-algebra of C(K) precisely as those with a positive approximate identity (eγ) such that x∗(eγ) → ⃦x∗⃦ for every positive functional x∗. We also show that every Banach lattice algebra with identity other than C(K) admits different product operations which are compatible with the order and the algebraic identity. This complements the classical result, due to Martignon, that on C(K) spaces pointwise multiplication is the unique compatible product. © 2025 American Mathematical Society.
publishDate 2025
dc.date.none.fl_str_mv 2025
2026
2026
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Preprint
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/420831
https://www.scopus.com/inward/record.uri?eid=2-s2.0-105006528300&doi=10.1090%2Fproc%2F17173&partnerID=40&md5=d00c076d1ad0bee679945ba21887a78b
url http://hdl.handle.net/10261/420831
https://www.scopus.com/inward/record.uri?eid=2-s2.0-105006528300&doi=10.1090%2Fproc%2F17173&partnerID=40&md5=d00c076d1ad0bee679945ba21887a78b
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Proceedings of the American Mathematical Society
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.81155

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