On normal operator logarithms

Autores
Chiumiento, Eduardo Hernan
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=e^Y.  If the spectra of X and Y are contained in the  strip S of the complex plane defined by |Im(z)|leq pi, 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=e^Y.
If X is an unbounded self-adjoint operator, which does not have  (2k+1) pi, k in Z,  as eigenvalues, and Y is normal with spectrum in S satisfying e^{iX}=e^Y, then Y in {  e^{iX} }´´. We  give alternative proofs and generalizations of results on normal operator exponentials proved by Ch. Schmoeger.
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina
Materia
Exponential Map
Normal Operator
Spectral Theorem
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/3374
Acceder
id CONICETDig_c950e7d0e4de561a56297cbab86e401a
oai_identifier_str oai:ri.conicet.gov.ar:11336/3374
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling On normal operator logarithmsChiumiento, Eduardo HernanExponential MapNormal OperatorSpectral Theoremhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let X,Y be normal bounded operators on a Hilbert space such that e^X=e^Y.  If the spectra of X and Y are contained in the  strip S of the complex plane defined by |Im(z)|leq pi, 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=e^Y. <br />If X is an unbounded self-adjoint operator, which does not have  (2k+1) pi, k in Z,  as eigenvalues, and Y is normal with spectrum in S satisfying e^{iX}=e^Y, then Y in {  e^{iX} }´´. We  give alternative proofs and generalizations of results on normal operator exponentials proved by Ch. Schmoeger.Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; ArgentinaElsevier Science Inc2013-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/3374Chiumiento, Eduardo Hernan; On normal operator logarithms; Elsevier Science Inc; Linear Algebra And Its Applications; 439; 7-2013; 455-4620024-3795enginfo:eu-repo/semantics/altIdentifier/doi/info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2013.03.026info:eu-repo/semantics/altIdentifier/url/http://www.journals.elsevier.com/linear-algebra-and-its-applications/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:03:23Zoai:ri.conicet.gov.ar:11336/3374instacron: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:34982025-10-22 12:03:23.472CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On normal operator logarithms
title On normal operator logarithms
spellingShingle On normal operator logarithms
Chiumiento, Eduardo Hernan
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 Hernan
author Chiumiento, Eduardo Hernan
author_facet Chiumiento, Eduardo Hernan
author_role author
dc.subject.none.fl_str_mv Exponential Map
Normal Operator
Spectral Theorem
topic Exponential Map
Normal Operator
Spectral Theorem
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let X,Y be normal bounded operators on a Hilbert space such that e^X=e^Y.  If the spectra of X and Y are contained in the  strip S of the complex plane defined by |Im(z)|leq pi, 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=e^Y. <br />If X is an unbounded self-adjoint operator, which does not have  (2k+1) pi, k in Z,  as eigenvalues, and Y is normal with spectrum in S satisfying e^{iX}=e^Y, then Y in {  e^{iX} }´´. We  give alternative proofs and generalizations of results on normal operator exponentials proved by Ch. Schmoeger.
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática; Argentina
description Let X,Y be normal bounded operators on a Hilbert space such that e^X=e^Y.  If the spectra of X and Y are contained in the  strip S of the complex plane defined by |Im(z)|leq pi, 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=e^Y. <br />If X is an unbounded self-adjoint operator, which does not have  (2k+1) pi, k in Z,  as eigenvalues, and Y is normal with spectrum in S satisfying e^{iX}=e^Y, then Y in {  e^{iX} }´´. We  give alternative proofs and generalizations of results on normal operator exponentials proved by Ch. Schmoeger.
publishDate 2013
dc.date.none.fl_str_mv 2013-07
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/11336/3374
Chiumiento, Eduardo Hernan; On normal operator logarithms; Elsevier Science Inc; Linear Algebra And Its Applications; 439; 7-2013; 455-462
0024-3795
url http://hdl.handle.net/11336/3374
identifier_str_mv Chiumiento, Eduardo Hernan; On normal operator logarithms; Elsevier Science Inc; Linear Algebra And Its Applications; 439; 7-2013; 455-462
0024-3795
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.laa.2013.03.026
info:eu-repo/semantics/altIdentifier/url/http://www.journals.elsevier.com/linear-algebra-and-its-applications/
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science Inc
publisher.none.fl_str_mv Elsevier Science Inc
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
_version_ 1846782375562838016
score 12.982451

Publicaciones similares