Riemannian geometry of finite rank positive operators
A riemannian metric is introduced in the infinite dimensional manifold Σ_n of positive operators with rank n<∞ on a Hilbert space H. The geometry of this manifold is studied and related to the geometry of the submanifolds Σ_p$ of positive operators with range equal to the range of a projection p...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2005 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/104393 |
| Acceso en línea: | http://hdl.handle.net/11336/104393 |
| Access Level: | acceso abierto |
| Palabra clave: | POSITIVE OPERATOR FINITE RANK PROJECTION https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | A riemannian metric is introduced in the infinite dimensional manifold Σ_n of positive operators with rank n<∞ on a Hilbert space H. The geometry of this manifold is studied and related to the geometry of the submanifolds Σ_p$ of positive operators with range equal to the range of a projection p (rank of p =n), and P_p of selfadjoint projections in the connected component of p. It is shown that these spaces are complete in the geodesic distance. |
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