Strict Singularity: A Lattice Approach

Given a Banach lattice E and a Banach space Y  we say that a bounded linear operator T : E → Y  is lattice strictly singular (disjointly strictly singular) if it fails to be invertible on any infinite-dimensional sublattice of E (on the span of any pairwise disjoint sequence in E). This is a survey...

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Detalhes bibliográficos
Autores: Flores, Julio, Hernández, Francisco L., Tradacete, Pedro
Formato: otro
Estado:Versión aceptada para publicación
Fecha de publicación:2019
País:España
Recursos:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/204188
Acesso em linha:http://hdl.handle.net/10261/204188
Access Level:acceso abierto
Palavra-chave:Disjointly strictly singular operator
Lattice strictly singular operator
Banach lattice
Unconditional basic sequence
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spelling Strict Singularity: A Lattice ApproachFlores, JulioHernández, Francisco L.Tradacete, PedroDisjointly strictly singular operatorLattice strictly singular operatorBanach latticeUnconditional basic sequenceGiven a Banach lattice E and a Banach space Y  we say that a bounded linear operator T : E → Y  is lattice strictly singular (disjointly strictly singular) if it fails to be invertible on any infinite-dimensional sublattice of E (on the span of any pairwise disjoint sequence in E). This is a survey on the existing answers up to the present day to the following questions: Is every lattice strictly singular operator also disjointly strictly singular? Do lattice strictly singular operators have a vector space structure?Support by the Spanish Government Grant No. MTM2016-76808-P is gratefully acknowledged. The third author also acknowledges the financial support from the Spanish Ministry of Economy and Competitiveness through Grant No. MTM2016-75196-P and the “Severo Ochoa Programme for Centres of Excellence in R&D” (SEV-2015-0554).Birkhäuser VerlagMinisterio de Economía, Industria y Competitividad (España)Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]2020202020192020info:eu-repo/semantics/otherhttp://purl.org/coar/resource_type/c_3248Postprintinfo:eu-repo/semantics/acceptedVersioninfo:eu-repo/semantics/bookParthttp://hdl.handle.net/10261/204188reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2016-75196-Pinfo:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/SEV-2015-0554http://dx.doi.org/10.1007/978-3-030-10850-2Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/2041882026-05-22T06:33:51Z
dc.title.none.fl_str_mv Strict Singularity: A Lattice Approach
title Strict Singularity: A Lattice Approach
spellingShingle Strict Singularity: A Lattice Approach
Flores, Julio
Disjointly strictly singular operator
Lattice strictly singular operator
Banach lattice
Unconditional basic sequence
title_short Strict Singularity: A Lattice Approach
title_full Strict Singularity: A Lattice Approach
title_fullStr Strict Singularity: A Lattice Approach
title_full_unstemmed Strict Singularity: A Lattice Approach
title_sort Strict Singularity: A Lattice Approach
dc.creator.none.fl_str_mv Flores, Julio
Hernández, Francisco L.
Tradacete, Pedro
author Flores, Julio
author_facet Flores, Julio
Hernández, Francisco L.
Tradacete, Pedro
author_role author
author2 Hernández, Francisco L.
Tradacete, Pedro
author2_role author
author
dc.contributor.none.fl_str_mv Ministerio de Economía, Industria y Competitividad (España)
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Disjointly strictly singular operator
Lattice strictly singular operator
Banach lattice
Unconditional basic sequence
topic Disjointly strictly singular operator
Lattice strictly singular operator
Banach lattice
Unconditional basic sequence
description Given a Banach lattice E and a Banach space Y  we say that a bounded linear operator T : E → Y  is lattice strictly singular (disjointly strictly singular) if it fails to be invertible on any infinite-dimensional sublattice of E (on the span of any pairwise disjoint sequence in E). This is a survey on the existing answers up to the present day to the following questions: Is every lattice strictly singular operator also disjointly strictly singular? Do lattice strictly singular operators have a vector space structure?
publishDate 2019
dc.date.none.fl_str_mv 2019
2020
2020
2020
dc.type.none.fl_str_mv info:eu-repo/semantics/other
http://purl.org/coar/resource_type/c_3248
Postprint
info:eu-repo/semantics/acceptedVersion
dc.type.openaire.fl_str_mv info:eu-repo/semantics/bookPart
format other
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/204188
url http://hdl.handle.net/10261/204188
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
#PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2016-75196-P
info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/SEV-2015-0554
http://dx.doi.org/10.1007/978-3-030-10850-2
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Birkhäuser Verlag
publisher.none.fl_str_mv Birkhäuser Verlag
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 15,811543

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