Projections with fixed difference : a Hopf-Rinow theorem
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
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| Formato: | Artículo publishedVersion |
| Lenguaje: | Inglés |
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Elsevier Science
2024
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| Acceso en línea: | http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1804 |
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I71-R177-UNGS-1804 |
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I71-R177-UNGS-18042024-12-23T13:21:47Z Projections with fixed difference : a Hopf-Rinow theorem Andruchow, Esteban Corach, Gustavo Recht, Lázaro Projections Pairs of projections Differences of projections Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina. Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina. Fil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina. The set D_A0 , of pairs of orthogonal projections (P,Q) in generic position with fixed difference P?Q=A_0, is shown to be a homogeneous smooth manifold: it is the quotient of the unitary group of the commutant {A_0}' divided by the unitary subgroup of the commutant {P0,Q0}', where (P0,Q0) is any fixed pair in D_A0. Endowed with a natural reductive structure (a linear connection) and the quotient Finsler metric of the operator norm, it behaves as a classic Riemannian space: any two pairs in D_A0 are joined by a geodesic of minimal length. Given a base pair (P0,Q0), pairs in an open dense subset of DA0 can be joined to (P0,Q0) by a unique minimal geodesic. 2024-12-23T13:21:47Z 2024-12-23T13:21:47Z 2019 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion Andruchow, E., Corach, G. y Recht, L. (2019). Projections with fixed difference: a Hopf-Rinow theorem. Differential Geometry and its Applications, 66, 155-180. 0926-2245 http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1804 eng http://dx.doi.org/10.1016/j.difgeo.2019.06.003 info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf application/pdf Elsevier Science Differential Geometry and its Applications. 2019; 66: 155-180 https://www.sciencedirect.com/journal/differential-geometry-and-its-applications/vol/66/suppl/C |
| institution |
Universidad Nacional de General Sarmiento |
| institution_str |
I-71 |
| repository_str |
R-177 |
| collection |
Repositorio Institucional Digital de Acceso Abierto (UNGS) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| topic |
Projections Pairs of projections Differences of projections |
| spellingShingle |
Projections Pairs of projections Differences of projections Andruchow, Esteban Corach, Gustavo Recht, Lázaro Projections with fixed difference : a Hopf-Rinow theorem |
| topic_facet |
Projections Pairs of projections Differences of projections |
| description |
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. |
| format |
Artículo Artículo publishedVersion |
| author |
Andruchow, Esteban Corach, Gustavo Recht, Lázaro |
| author_facet |
Andruchow, Esteban Corach, Gustavo Recht, Lázaro |
| author_sort |
Andruchow, Esteban |
| title |
Projections with fixed difference : a Hopf-Rinow theorem |
| title_short |
Projections with fixed difference : a Hopf-Rinow theorem |
| title_full |
Projections with fixed difference : a Hopf-Rinow theorem |
| title_fullStr |
Projections with fixed difference : a Hopf-Rinow theorem |
| title_full_unstemmed |
Projections with fixed difference : a Hopf-Rinow theorem |
| title_sort |
projections with fixed difference : a hopf-rinow theorem |
| publisher |
Elsevier Science |
| publishDate |
2024 |
| url |
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1804 |
| work_keys_str_mv |
AT andruchowesteban projectionswithfixeddifferenceahopfrinowtheorem AT corachgustavo projectionswithfixeddifferenceahopfrinowtheorem AT rechtlazaro projectionswithfixeddifferenceahopfrinowtheorem |
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1824528739356114944 |