On the geometry of generalized inverses
- Autores
- Andruchow, Esteban; Corach, Gustavo; Mbekhta, Mostafa
- Año de publicación
- 2005
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We study the set S = {(a, b) ∈ A × A : aba = a, bab = b} which pairs the relatively regular elements of aBanach algebra A with their pseudoinverses, and prove that it is an analytic submanifold of A × A. If A is a C∗-algebra, inside S lies a copy the set I of partial isometries, we prove that this set is a C∞ submanifold of S (as well as a submanifold of A). These manifolds carry actions from, respectively, G_A × G_A and U_A ×U_A, where G_A is the group of invertibles of A and U_A is the subgroup of unitary elements. These actions define homogeneous reductive structures for S and I (in the differential geometric sense). Certain topological and homotopical properties of these sets are derived. In particular, it is shown that if A is a von Neumann algebra and p is a purely infinite projection of A, then the connected component I_p of p in I is simply connected. If 1 − p is also purely infinite, then I_p is contractible.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Mbekhta, Mostafa. Universite Lille; Francia - Materia
-
RELATIVELY REGULAR
PARTIAL ISOMETRY - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/106942
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On the geometry of generalized inversesAndruchow, EstebanCorach, GustavoMbekhta, MostafaRELATIVELY REGULARPARTIAL ISOMETRYhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the set S = {(a, b) ∈ A × A : aba = a, bab = b} which pairs the relatively regular elements of aBanach algebra A with their pseudoinverses, and prove that it is an analytic submanifold of A × A. If A is a C∗-algebra, inside S lies a copy the set I of partial isometries, we prove that this set is a C∞ submanifold of S (as well as a submanifold of A). These manifolds carry actions from, respectively, G_A × G_A and U_A ×U_A, where G_A is the group of invertibles of A and U_A is the subgroup of unitary elements. These actions define homogeneous reductive structures for S and I (in the differential geometric sense). Certain topological and homotopical properties of these sets are derived. In particular, it is shown that if A is a von Neumann algebra and p is a purely infinite projection of A, then the connected component I_p of p in I is simply connected. If 1 − p is also purely infinite, then I_p is contractible.Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Mbekhta, Mostafa. Universite Lille; FranciaWiley VCH Verlag2005-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/106942Andruchow, Esteban; Corach, Gustavo; Mbekhta, Mostafa; On the geometry of generalized inverses; Wiley VCH Verlag; Mathematische Nachrichten; 278; 7-8; 4-2005; 756-7700025-584X1522-2616CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1002/mana.200310270info:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/abs/10.1002/mana.200310270info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:46:53Zoai:ri.conicet.gov.ar:11336/106942instacron: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 09:46:53.873CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
On the geometry of generalized inverses |
| title |
On the geometry of generalized inverses |
| spellingShingle |
On the geometry of generalized inverses Andruchow, Esteban RELATIVELY REGULAR PARTIAL ISOMETRY |
| title_short |
On the geometry of generalized inverses |
| title_full |
On the geometry of generalized inverses |
| title_fullStr |
On the geometry of generalized inverses |
| title_full_unstemmed |
On the geometry of generalized inverses |
| title_sort |
On the geometry of generalized inverses |
| dc.creator.none.fl_str_mv |
Andruchow, Esteban Corach, Gustavo Mbekhta, Mostafa |
| author |
Andruchow, Esteban |
| author_facet |
Andruchow, Esteban Corach, Gustavo Mbekhta, Mostafa |
| author_role |
author |
| author2 |
Corach, Gustavo Mbekhta, Mostafa |
| author2_role |
author author |
| dc.subject.none.fl_str_mv |
RELATIVELY REGULAR PARTIAL ISOMETRY |
| topic |
RELATIVELY REGULAR PARTIAL ISOMETRY |
| 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 S = {(a, b) ∈ A × A : aba = a, bab = b} which pairs the relatively regular elements of aBanach algebra A with their pseudoinverses, and prove that it is an analytic submanifold of A × A. If A is a C∗-algebra, inside S lies a copy the set I of partial isometries, we prove that this set is a C∞ submanifold of S (as well as a submanifold of A). These manifolds carry actions from, respectively, G_A × G_A and U_A ×U_A, where G_A is the group of invertibles of A and U_A is the subgroup of unitary elements. These actions define homogeneous reductive structures for S and I (in the differential geometric sense). Certain topological and homotopical properties of these sets are derived. In particular, it is shown that if A is a von Neumann algebra and p is a purely infinite projection of A, then the connected component I_p of p in I is simply connected. If 1 − p is also purely infinite, then I_p is contractible. Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina Fil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina Fil: Mbekhta, Mostafa. Universite Lille; Francia |
| description |
We study the set S = {(a, b) ∈ A × A : aba = a, bab = b} which pairs the relatively regular elements of aBanach algebra A with their pseudoinverses, and prove that it is an analytic submanifold of A × A. If A is a C∗-algebra, inside S lies a copy the set I of partial isometries, we prove that this set is a C∞ submanifold of S (as well as a submanifold of A). These manifolds carry actions from, respectively, G_A × G_A and U_A ×U_A, where G_A is the group of invertibles of A and U_A is the subgroup of unitary elements. These actions define homogeneous reductive structures for S and I (in the differential geometric sense). Certain topological and homotopical properties of these sets are derived. In particular, it is shown that if A is a von Neumann algebra and p is a purely infinite projection of A, then the connected component I_p of p in I is simply connected. If 1 − p is also purely infinite, then I_p is contractible. |
| publishDate |
2005 |
| dc.date.none.fl_str_mv |
2005-04 |
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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 |
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http://hdl.handle.net/11336/106942 Andruchow, Esteban; Corach, Gustavo; Mbekhta, Mostafa; On the geometry of generalized inverses; Wiley VCH Verlag; Mathematische Nachrichten; 278; 7-8; 4-2005; 756-770 0025-584X 1522-2616 CONICET Digital CONICET |
| url |
http://hdl.handle.net/11336/106942 |
| identifier_str_mv |
Andruchow, Esteban; Corach, Gustavo; Mbekhta, Mostafa; On the geometry of generalized inverses; Wiley VCH Verlag; Mathematische Nachrichten; 278; 7-8; 4-2005; 756-770 0025-584X 1522-2616 CONICET Digital CONICET |
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eng |
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eng |
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info:eu-repo/semantics/altIdentifier/doi/10.1002/mana.200310270 info:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/abs/10.1002/mana.200310270 |
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openAccess |
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Wiley VCH Verlag |
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Wiley VCH Verlag |
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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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