The Coburn Lemma and the Hartman–Wintner–Simonenko Theorem for Toeplitz Operators on Abstract Hardy 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/10362/155251
Resumo: Publisher Copyright: © 2023, The Author(s).
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spelling The Coburn Lemma and the Hartman–Wintner–Simonenko Theorem for Toeplitz Operators on Abstract Hardy SpacesBanach function spaceCoburn’s lemmaFredholmnessInvertibilityNormal solvabilityToeplitz operatorAnalysisAlgebra and Number TheoryPublisher Copyright: © 2023, The Author(s).Let X be a Banach function space on the unit circle T, let X′ be its associate space, and let H[X] and H[X′] be the abstract Hardy spaces built upon X and X′, respectively. Suppose that the Riesz projection P is bounded on X and a∈ L∞\ { 0 }. We show that P is bounded on X′. So, we can consider the Toeplitz operators T(a) f= P(af) and T(a¯) g= P(a¯ g) on H[X] and H[X′] , respectively. In our previous paper, we have shown that if X is not separable, then one cannot rephrase Coburn’s lemma as in the case of classical Hardy spaces Hp, 1 < p< ∞, and guarantee that T(a) has a trivial kernel or a dense range on H[X]. The first main result of the present paper is the following extension of Coburn’s lemma: the kernel of T(a) or the kernel of T(a¯) is trivial. The second main result is a generalisation of the Hartman–Wintner–Simonenko theorem saying that if T(a) is normally solvable on the space H[X], then 1 / a∈ L∞.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNKarlovych, OleksiyShargorodsky, Eugene2023-07-13T22:18:30Z2023-032023-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article17application/pdfhttp://hdl.handle.net/10362/155251eng0378-620XPURE: 66129793https://doi.org/10.1007/s00020-023-02725-8info: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:RCAAP2024-03-11T05:37:48Zoai:run.unl.pt:10362/155251Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T03:55:59.843699Repositório 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 The Coburn Lemma and the Hartman–Wintner–Simonenko Theorem for Toeplitz Operators on Abstract Hardy Spaces
title The Coburn Lemma and the Hartman–Wintner–Simonenko Theorem for Toeplitz Operators on Abstract Hardy Spaces
spellingShingle The Coburn Lemma and the Hartman–Wintner–Simonenko Theorem for Toeplitz Operators on Abstract Hardy Spaces
Karlovych, Oleksiy
Banach function space
Coburn’s lemma
Fredholmness
Invertibility
Normal solvability
Toeplitz operator
Analysis
Algebra and Number Theory
title_short The Coburn Lemma and the Hartman–Wintner–Simonenko Theorem for Toeplitz Operators on Abstract Hardy Spaces
title_full The Coburn Lemma and the Hartman–Wintner–Simonenko Theorem for Toeplitz Operators on Abstract Hardy Spaces
title_fullStr The Coburn Lemma and the Hartman–Wintner–Simonenko Theorem for Toeplitz Operators on Abstract Hardy Spaces
title_full_unstemmed The Coburn Lemma and the Hartman–Wintner–Simonenko Theorem for Toeplitz Operators on Abstract Hardy Spaces
title_sort The Coburn Lemma and the Hartman–Wintner–Simonenko Theorem for Toeplitz Operators on Abstract Hardy 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 Banach function space
Coburn’s lemma
Fredholmness
Invertibility
Normal solvability
Toeplitz operator
Analysis
Algebra and Number Theory
topic Banach function space
Coburn’s lemma
Fredholmness
Invertibility
Normal solvability
Toeplitz operator
Analysis
Algebra and Number Theory
description Publisher Copyright: © 2023, The Author(s).
publishDate 2023
dc.date.none.fl_str_mv 2023-07-13T22:18:30Z
2023-03
2023-03-01T00:00:00Z
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/10362/155251
url http://hdl.handle.net/10362/155251
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0378-620X
PURE: 66129793
https://doi.org/10.1007/s00020-023-02725-8
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 17
application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
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instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
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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
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