Invariant subspaces for positive operators on Banach spaces with unconditional basis

We prove that every lattice homomorphism acting on a Banach space X with the lattice structure given by an unconditional basis has a non-trivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal, which is no longer true for every positive operator on such a space. Motiv...

Descripción completa

Detalles Bibliográficos
Autores: Gallardo Gutiérrez, Eva Antonia, González Doña, Javier, Tradacete Pérez, Pedro
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/71793
Acceso en línea:https://hdl.handle.net/20.500.14352/71793
Access Level:acceso abierto
Palabra clave:517.982.22
Banach lattices
Lattice homomorphisms
Invariant subspaces
Invariant ideals
Análisis funcional y teoría de operadores
id ES_4ce0522b5aa5830ee8af1ef0ce4e6e7c
oai_identifier_str oai:docta.ucm.es:20.500.14352/71793
network_acronym_str ES
network_name_str España
repository_id_str
spelling Invariant subspaces for positive operators on Banach spaces with unconditional basisGallardo Gutiérrez, Eva AntoniaGonzález Doña, JavierTradacete Pérez, Pedro517.982.22Banach latticesLattice homomorphismsInvariant subspacesInvariant idealsAnálisis funcional y teoría de operadoresWe prove that every lattice homomorphism acting on a Banach space X with the lattice structure given by an unconditional basis has a non-trivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal, which is no longer true for every positive operator on such a space. Motivated by these examples, we characterize tridiagonal positive operators without non-trivial closed invariant ideals on X extending to this context a result of Grivaux on the existence of non-trivial closed invariant subspaces for tridiagonal operators.American Mathematical SocietyUniversidad Complutense de Madrid20222022-06-1620222022-06-16journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/71793reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/717932026-06-02T12:44:21Z
dc.title.none.fl_str_mv Invariant subspaces for positive operators on Banach spaces with unconditional basis
title Invariant subspaces for positive operators on Banach spaces with unconditional basis
spellingShingle Invariant subspaces for positive operators on Banach spaces with unconditional basis
Gallardo Gutiérrez, Eva Antonia
517.982.22
Banach lattices
Lattice homomorphisms
Invariant subspaces
Invariant ideals
Análisis funcional y teoría de operadores
title_short Invariant subspaces for positive operators on Banach spaces with unconditional basis
title_full Invariant subspaces for positive operators on Banach spaces with unconditional basis
title_fullStr Invariant subspaces for positive operators on Banach spaces with unconditional basis
title_full_unstemmed Invariant subspaces for positive operators on Banach spaces with unconditional basis
title_sort Invariant subspaces for positive operators on Banach spaces with unconditional basis
dc.creator.none.fl_str_mv Gallardo Gutiérrez, Eva Antonia
González Doña, Javier
Tradacete Pérez, Pedro
author Gallardo Gutiérrez, Eva Antonia
author_facet Gallardo Gutiérrez, Eva Antonia
González Doña, Javier
Tradacete Pérez, Pedro
author_role author
author2 González Doña, Javier
Tradacete Pérez, Pedro
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517.982.22
Banach lattices
Lattice homomorphisms
Invariant subspaces
Invariant ideals
Análisis funcional y teoría de operadores
topic 517.982.22
Banach lattices
Lattice homomorphisms
Invariant subspaces
Invariant ideals
Análisis funcional y teoría de operadores
description We prove that every lattice homomorphism acting on a Banach space X with the lattice structure given by an unconditional basis has a non-trivial closed invariant subspace. In fact, it has a non-trivial closed invariant ideal, which is no longer true for every positive operator on such a space. Motivated by these examples, we characterize tridiagonal positive operators without non-trivial closed invariant ideals on X extending to this context a result of Grivaux on the existence of non-trivial closed invariant subspaces for tridiagonal operators.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-06-16
2022
2022-06-16
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/71793
url https://hdl.handle.net/20.500.14352/71793
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
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
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869407655547633664
score 15,300719

Similares en LA Referencia