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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/109495
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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 Técnicas2025-09-29T09:45:14Zoai: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:34982025-09-29 09:45:14.341CONICET 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 |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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13.070432 |