A note on a question by T. Ando

Autores
Andruchow, Esteban
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In 1979 T. Ando posed the following question: suppose E and F are two projectionvalued measures defined on an algebra Σ of subsets of Ω, which verifykE(∆) − F(∆)k ≤ 1 − δ, ∆ ∈ Σ,for some δ > 0. Does there exist a unitary operator u such that u∗E(∆)u = F(∆) for all∆ ∈ Σ? He knew that the answer was affirmative if both measures were strongly σ-additiveand maximal (i.e. E and F have ciclic vectors). In this note, we show that the answer isalso affirmative if both measures take values in a common finite von Neumann algebra.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de General Sarmiento; Argentina
Materia
Spectral measure
Unitary equivalence
Finite algebra
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
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spelling A note on a question by T. AndoAndruchow, EstebanSpectral measureUnitary equivalenceFinite algebrahttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In 1979 T. Ando posed the following question: suppose E and F are two projectionvalued measures defined on an algebra Σ of subsets of Ω, which verifykE(∆) − F(∆)k ≤ 1 − δ, ∆ ∈ Σ,for some δ > 0. Does there exist a unitary operator u such that u∗E(∆)u = F(∆) for all∆ ∈ Σ? He knew that the answer was affirmative if both measures were strongly σ-additiveand maximal (i.e. E and F have ciclic vectors). In this note, we show that the answer isalso affirmative if both measures take values in a common finite von Neumann algebra.Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de General Sarmiento; ArgentinaUniversity of Szeged. Bolyai Institute2014-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18941Andruchow, Esteban; A note on a question by T. Ando; University of Szeged. Bolyai Institute; Acta Scientiarum Mathematicarum (szeged); 80; 3-4; 11-2014; 651-6580001-6969CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://pub.acta.hu/acta/showCustomerArticle.action?id=38878&dataObjectType=article&returnAction=showCustomerVolume&sessionDataSetId=400e733b855873aa&style=info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:53:19Zoai:ri.conicet.gov.ar:11336/18941instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-11-12 09:53:19.903CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A note on a question by T. Ando
title A note on a question by T. Ando
spellingShingle A note on a question by T. Ando
Andruchow, Esteban
Spectral measure
Unitary equivalence
Finite algebra
title_short A note on a question by T. Ando
title_full A note on a question by T. Ando
title_fullStr A note on a question by T. Ando
title_full_unstemmed A note on a question by T. Ando
title_sort A note on a question by T. Ando
dc.creator.none.fl_str_mv Andruchow, Esteban
author Andruchow, Esteban
author_facet Andruchow, Esteban
author_role author
dc.subject.none.fl_str_mv Spectral measure
Unitary equivalence
Finite algebra
topic Spectral measure
Unitary equivalence
Finite algebra
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In 1979 T. Ando posed the following question: suppose E and F are two projectionvalued measures defined on an algebra Σ of subsets of Ω, which verifykE(∆) − F(∆)k ≤ 1 − δ, ∆ ∈ Σ,for some δ > 0. Does there exist a unitary operator u such that u∗E(∆)u = F(∆) for all∆ ∈ Σ? He knew that the answer was affirmative if both measures were strongly σ-additiveand maximal (i.e. E and F have ciclic vectors). In this note, we show that the answer isalso affirmative if both measures take values in a common finite von Neumann algebra.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de General Sarmiento; Argentina
description In 1979 T. Ando posed the following question: suppose E and F are two projectionvalued measures defined on an algebra Σ of subsets of Ω, which verifykE(∆) − F(∆)k ≤ 1 − δ, ∆ ∈ Σ,for some δ > 0. Does there exist a unitary operator u such that u∗E(∆)u = F(∆) for all∆ ∈ Σ? He knew that the answer was affirmative if both measures were strongly σ-additiveand maximal (i.e. E and F have ciclic vectors). In this note, we show that the answer isalso affirmative if both measures take values in a common finite von Neumann algebra.
publishDate 2014
dc.date.none.fl_str_mv 2014-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/18941
Andruchow, Esteban; A note on a question by T. Ando; University of Szeged. Bolyai Institute; Acta Scientiarum Mathematicarum (szeged); 80; 3-4; 11-2014; 651-658
0001-6969
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18941
identifier_str_mv Andruchow, Esteban; A note on a question by T. Ando; University of Szeged. Bolyai Institute; Acta Scientiarum Mathematicarum (szeged); 80; 3-4; 11-2014; 651-658
0001-6969
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://pub.acta.hu/acta/showCustomerArticle.action?id=38878&dataObjectType=article&returnAction=showCustomerVolume&sessionDataSetId=400e733b855873aa&style=
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv University of Szeged. Bolyai Institute
publisher.none.fl_str_mv University of Szeged. Bolyai Institute
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.976206

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