Essentially orthogonal subspaces
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
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| Formato: | Artículo publishedVersion |
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Theta Foundation
2024
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| Acceso en línea: | http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1808 |
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I71-R177-UNGS-1808 |
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I71-R177-UNGS-18082024-12-23T13:21:48Z Essentially orthogonal subspaces Andruchow, Esteban Corach, Gustavo Projections Pairs of projections Compact operators Grasmann manifold 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. We study the set C consisting of pairs of orthogonal projectionsP,Q acting in a Hilbert space H such that PQ is a compact operator. Thesepairs have a rich geometric structure which we describe here. They are partitionedin three subclasses: C0 consists of pairs where P or Q have finite rank,C1 of pairs such that Q lies in the restricted Grassmannian (also called Sato-Grassmannian) of the polarization H = N(P)? R(P), and C?. We characterize the connected components of these classes: the components of C0 are parametrized by the rank, the components of C1 are parametrized by the Fredholm index of the pairs, and C? is connected. We show that these subsets are(non-complemented) differentiable submanifolds of B(H) x B(H). 2024-12-23T13:21:48Z 2024-12-23T13:21:48Z 2018 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion Andruchow, E. y Corach, G. (2018). Essentially orthogonal subspaces. Journal Of Operator Theory, 79(1), 79-100. 0379-4024 http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1808 eng 10.7900/jot.2016dec13.2138 info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf application/pdf Theta Foundation Journal Of Operator Theory. Ene. 2018; 79(1): 79-100 https://www.theta.ro/jot/archive/2018-079-001/index_2018-079-001.html |
| 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 Compact operators Grasmann manifold |
| spellingShingle |
Projections Pairs of projections Compact operators Grasmann manifold Andruchow, Esteban Corach, Gustavo Essentially orthogonal subspaces |
| topic_facet |
Projections Pairs of projections Compact operators Grasmann manifold |
| description |
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. |
| format |
Artículo Artículo publishedVersion |
| author |
Andruchow, Esteban Corach, Gustavo |
| author_facet |
Andruchow, Esteban Corach, Gustavo |
| author_sort |
Andruchow, Esteban |
| title |
Essentially orthogonal subspaces |
| title_short |
Essentially orthogonal subspaces |
| title_full |
Essentially orthogonal subspaces |
| title_fullStr |
Essentially orthogonal subspaces |
| title_full_unstemmed |
Essentially orthogonal subspaces |
| title_sort |
essentially orthogonal subspaces |
| publisher |
Theta Foundation |
| publishDate |
2024 |
| url |
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1808 |
| work_keys_str_mv |
AT andruchowesteban essentiallyorthogonalsubspaces AT corachgustavo essentiallyorthogonalsubspaces |
| _version_ |
1824528741459558400 |