On normal operator logarithms

Autores
Chiumiento, Eduardo Hernán
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let X,Y be normal bounded operators on a Hilbert space such that e X=eY. If the spectra of X and Y are contained in the strip S of the complex plane defined by |I(z)|≤π, we show that |X|=|Y|. If Y is only assumed to be bounded, then |X|Y=Y|X|. We give a formula for X-Y in terms of spectral projections of X and Y provided that X,Y are normal and e X=eY. If X is an unbounded self-adjoint operator, which does not have (2k+1)π,k∈ℤ, as eigenvalues, and Y is normal with spectrum in S satisfying eiX=eY, then Y∈{ e iX}″. We give alternative proofs and generalizations of results on normal operator exponentials proved by Schmoeger.
Facultad de Ciencias Exactas
Materia
Matemática
Exponential map
Normal operator
Spectral theorem
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/85121
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/85121
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
spelling On normal operator logarithmsChiumiento, Eduardo HernánMatemáticaExponential mapNormal operatorSpectral theoremLet X,Y be normal bounded operators on a Hilbert space such that e X=eY. If the spectra of X and Y are contained in the strip S of the complex plane defined by |I(z)|≤π, we show that |X|=|Y|. If Y is only assumed to be bounded, then |X|Y=Y|X|. We give a formula for X-Y in terms of spectral projections of X and Y provided that X,Y are normal and e X=eY. If X is an unbounded self-adjoint operator, which does not have (2k+1)π,k∈ℤ, as eigenvalues, and Y is normal with spectrum in S satisfying eiX=eY, then Y∈{ e iX}″. We give alternative proofs and generalizations of results on normal operator exponentials proved by Schmoeger.Facultad de Ciencias Exactas2013info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf455-462http://sedici.unlp.edu.ar/handle/10915/85121enginfo:eu-repo/semantics/altIdentifier/issn/0024-3795info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2013.03.026info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-09-29T11:16:30Zoai:sedici.unlp.edu.ar:10915/85121Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:16:31.056SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv On normal operator logarithms
title On normal operator logarithms
spellingShingle On normal operator logarithms
Chiumiento, Eduardo Hernán
Matemática
Exponential map
Normal operator
Spectral theorem
title_short On normal operator logarithms
title_full On normal operator logarithms
title_fullStr On normal operator logarithms
title_full_unstemmed On normal operator logarithms
title_sort On normal operator logarithms
dc.creator.none.fl_str_mv Chiumiento, Eduardo Hernán
author Chiumiento, Eduardo Hernán
author_facet Chiumiento, Eduardo Hernán
author_role author
dc.subject.none.fl_str_mv Matemática
Exponential map
Normal operator
Spectral theorem
topic Matemática
Exponential map
Normal operator
Spectral theorem
dc.description.none.fl_txt_mv Let X,Y be normal bounded operators on a Hilbert space such that e X=eY. If the spectra of X and Y are contained in the strip S of the complex plane defined by |I(z)|≤π, we show that |X|=|Y|. If Y is only assumed to be bounded, then |X|Y=Y|X|. We give a formula for X-Y in terms of spectral projections of X and Y provided that X,Y are normal and e X=eY. If X is an unbounded self-adjoint operator, which does not have (2k+1)π,k∈ℤ, as eigenvalues, and Y is normal with spectrum in S satisfying eiX=eY, then Y∈{ e iX}″. We give alternative proofs and generalizations of results on normal operator exponentials proved by Schmoeger.
Facultad de Ciencias Exactas
description Let X,Y be normal bounded operators on a Hilbert space such that e X=eY. If the spectra of X and Y are contained in the strip S of the complex plane defined by |I(z)|≤π, we show that |X|=|Y|. If Y is only assumed to be bounded, then |X|Y=Y|X|. We give a formula for X-Y in terms of spectral projections of X and Y provided that X,Y are normal and e X=eY. If X is an unbounded self-adjoint operator, which does not have (2k+1)π,k∈ℤ, as eigenvalues, and Y is normal with spectrum in S satisfying eiX=eY, then Y∈{ e iX}″. We give alternative proofs and generalizations of results on normal operator exponentials proved by Schmoeger.
publishDate 2013
dc.date.none.fl_str_mv 2013
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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://sedici.unlp.edu.ar/handle/10915/85121
url http://sedici.unlp.edu.ar/handle/10915/85121
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/issn/0024-3795
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2013.03.026
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
455-462
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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score 13.070432

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