Nilpotents in finite algebras

Autores
Andruchow, Esteban; Stojanoff, Demetrio
Año de publicación
2003
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the set of nilpotents t (t^n=0) of a type $II_1 von Neumann  algebra A which verify that t^{n-1}+t* is invertible. These are shown to be all similar in A. The set of all such operators, named by D.A. Herrero very nice Jordan nilpotents, forms a simply connected smooth submanifold of A in the norm topology. Nilpotents are related to systems of projectors, i.e. n-tuples (p_1,...,p_n) of mutually orthogonal projections of the algebra which sum 1, via the map φ(t)=(P_{ker t},P_{ker t^2}-P_{ker t},...,P_{ker t^{n-1}}-P_{ker t^{n-2}},1-P_{ker t^{n-1}}). The properties of this map, called the canonical decomposition of nilpotents in the literature, are examined.
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
NILPOTENT OPERATOR
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
OAI Identificador
oai:ri.conicet.gov.ar:11336/109495
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Nilpotents in finite algebrasAndruchow, EstebanStojanoff, DemetrioNILPOTENT OPERATORFINITE ALGEBRAhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the set of nilpotents t (t^n=0) of a type $II_1 von Neumann  algebra A which verify that t^{n-1}+t* is invertible. These are shown to be all similar in A. The set of all such operators, named by D.A. Herrero very nice Jordan nilpotents, forms a simply connected smooth submanifold of A in the norm topology. Nilpotents are related to systems of projectors, i.e. n-tuples (p_1,...,p_n) of mutually orthogonal projections of the algebra which sum 1, via the map φ(t)=(P_{ker t},P_{ker t^2}-P_{ker t},...,P_{ker t^{n-1}}-P_{ker t^{n-2}},1-P_{ker t^{n-1}}). The properties of this map, called the canonical decomposition of nilpotents in the literature, are examined.Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Stojanoff, Demetrio. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaBirkhauser Verlag Ag2003-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/109495Andruchow, Esteban; Stojanoff, Demetrio; Nilpotents in finite algebras; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 45; 3; 3-2003; 251-2670378-620X1420-8989CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s000200300004info:eu-repo/semantics/altIdentifier/doi/10.1007/s000200300004info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:14:08Zoai:ri.conicet.gov.ar:11336/109495instacron: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 11:14:08.453CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Nilpotents in finite algebras
title Nilpotents in finite algebras
spellingShingle Nilpotents in finite algebras
Andruchow, Esteban
NILPOTENT OPERATOR
FINITE ALGEBRA
title_short Nilpotents in finite algebras
title_full Nilpotents in finite algebras
title_fullStr Nilpotents in finite algebras
title_full_unstemmed Nilpotents in finite algebras
title_sort Nilpotents in finite algebras
dc.creator.none.fl_str_mv Andruchow, Esteban
Stojanoff, Demetrio
author Andruchow, Esteban
author_facet Andruchow, Esteban
Stojanoff, Demetrio
author_role author
author2 Stojanoff, Demetrio
author2_role author
dc.subject.none.fl_str_mv NILPOTENT OPERATOR
FINITE ALGEBRA
topic NILPOTENT OPERATOR
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 We study the set of nilpotents t (t^n=0) of a type $II_1 von Neumann  algebra A which verify that t^{n-1}+t* is invertible. These are shown to be all similar in A. The set of all such operators, named by D.A. Herrero very nice Jordan nilpotents, forms a simply connected smooth submanifold of A in the norm topology. Nilpotents are related to systems of projectors, i.e. n-tuples (p_1,...,p_n) of mutually orthogonal projections of the algebra which sum 1, via the map φ(t)=(P_{ker t},P_{ker t^2}-P_{ker t},...,P_{ker t^{n-1}}-P_{ker t^{n-2}},1-P_{ker t^{n-1}}). The properties of this map, called the canonical decomposition of nilpotents in the literature, are examined.
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description We study the set of nilpotents t (t^n=0) of a type $II_1 von Neumann  algebra A which verify that t^{n-1}+t* is invertible. These are shown to be all similar in A. The set of all such operators, named by D.A. Herrero very nice Jordan nilpotents, forms a simply connected smooth submanifold of A in the norm topology. Nilpotents are related to systems of projectors, i.e. n-tuples (p_1,...,p_n) of mutually orthogonal projections of the algebra which sum 1, via the map φ(t)=(P_{ker t},P_{ker t^2}-P_{ker t},...,P_{ker t^{n-1}}-P_{ker t^{n-2}},1-P_{ker t^{n-1}}). The properties of this map, called the canonical decomposition of nilpotents in the literature, are examined.
publishDate 2003
dc.date.none.fl_str_mv 2003-03
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/11336/109495
Andruchow, Esteban; Stojanoff, Demetrio; Nilpotents in finite algebras; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 45; 3; 3-2003; 251-267
0378-620X
1420-8989
CONICET Digital
CONICET
url http://hdl.handle.net/11336/109495
identifier_str_mv Andruchow, Esteban; Stojanoff, Demetrio; Nilpotents in finite algebras; Birkhauser Verlag Ag; Integral Equations and Operator Theory; 45; 3; 3-2003; 251-267
0378-620X
1420-8989
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s000200300004
info:eu-repo/semantics/altIdentifier/doi/10.1007/s000200300004
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 Birkhauser Verlag Ag
publisher.none.fl_str_mv Birkhauser Verlag Ag
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 12.928904

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