On the weak convergence of shift operators to zero on rearrangement-invariant spaces

Detalhes bibliográficos
Autor(a) principal: Karlovych, Oleksiy
Data de Publicação: 2023
Outros Autores: Shargorodsky, Eugene
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10362/152251
Resumo: Publisher Copyright: © 2022, Universidad Complutense de Madrid.
id RCAP_80bc6cdb16d57f908329eb981ec2a02f
oai_identifier_str oai:run.unl.pt:10362/152251
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling On the weak convergence of shift operators to zero on rearrangement-invariant spacesFundamental functionLimit operatorMarcinkiewicz endpoint spaceNon-separable Orlicz spaceRearrangement-invariant Banach function spaceShift operatorWeak convergence to zeroMathematics(all)Publisher Copyright: © 2022, Universidad Complutense de Madrid.Let { hn} be a sequence in Rd tending to infinity and let {Thn} be the corresponding sequence of shift operators given by (Thnf)(x)=f(x-hn) for x∈ Rd. We prove that {Thn} converges weakly to the zero operator as n→ ∞ on a separable rearrangement-invariant Banach function space X(Rd) if and only if its fundamental function φX satisfies φX(t) / t→ 0 as t→ ∞. On the other hand, we show that {Thn} does not converge weakly to the zero operator as n→ ∞ on all Marcinkiewicz endpoint spaces Mφ(Rd) and on all non-separable Orlicz spaces LΦ(Rd). Finally, we prove that if { hn} is an arithmetic progression: hn= nh, n∈ N with an arbitrary h∈ Rd\ { 0 } , then { Tnh} does not converge weakly to the zero operator on any non-separable rearrangement-invariant Banach function space X(Rd) as n→ ∞.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNKarlovych, OleksiyShargorodsky, Eugene2024-01-02T01:31:34Z2023-012023-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article34application/pdfhttp://hdl.handle.net/10362/152251eng1139-1138PURE: 56423613https://doi.org/10.1007/s13163-022-00423-4info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-03-11T05:34:36Zoai:run.unl.pt:10362/152251Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:54:51.062032Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv On the weak convergence of shift operators to zero on rearrangement-invariant spaces
title On the weak convergence of shift operators to zero on rearrangement-invariant spaces
spellingShingle On the weak convergence of shift operators to zero on rearrangement-invariant spaces
Karlovych, Oleksiy
Fundamental function
Limit operator
Marcinkiewicz endpoint space
Non-separable Orlicz space
Rearrangement-invariant Banach function space
Shift operator
Weak convergence to zero
Mathematics(all)
title_short On the weak convergence of shift operators to zero on rearrangement-invariant spaces
title_full On the weak convergence of shift operators to zero on rearrangement-invariant spaces
title_fullStr On the weak convergence of shift operators to zero on rearrangement-invariant spaces
title_full_unstemmed On the weak convergence of shift operators to zero on rearrangement-invariant spaces
title_sort On the weak convergence of shift operators to zero on rearrangement-invariant spaces
author Karlovych, Oleksiy
author_facet Karlovych, Oleksiy
Shargorodsky, Eugene
author_role author
author2 Shargorodsky, Eugene
author2_role author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
DM - Departamento de Matemática
RUN
dc.contributor.author.fl_str_mv Karlovych, Oleksiy
Shargorodsky, Eugene
dc.subject.por.fl_str_mv Fundamental function
Limit operator
Marcinkiewicz endpoint space
Non-separable Orlicz space
Rearrangement-invariant Banach function space
Shift operator
Weak convergence to zero
Mathematics(all)
topic Fundamental function
Limit operator
Marcinkiewicz endpoint space
Non-separable Orlicz space
Rearrangement-invariant Banach function space
Shift operator
Weak convergence to zero
Mathematics(all)
description Publisher Copyright: © 2022, Universidad Complutense de Madrid.
publishDate 2023
dc.date.none.fl_str_mv 2023-01
2023-01-01T00:00:00Z
2024-01-02T01:31:34Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/152251
url http://hdl.handle.net/10362/152251
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1139-1138
PURE: 56423613
https://doi.org/10.1007/s13163-022-00423-4
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 34
application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
_version_ 1799138136635211776

Registros relacionados