Projective space of a C*-module
Let X be a right Hilbert C^*-module over A. We study the geometry and the topology of the projective space P(X) of X, consisting of the orthocomplemented submodules of X which are generated by a single element. We also study the geometry of the p-sphere S_p(X) and the natural fibration S_p(X) →P(X)...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2011 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/110303 |
| Acceso en línea: | http://hdl.handle.net/11336/110303 |
| Access Level: | acceso abierto |
| Palabra clave: | MODULO PROJECTIVE GEODESICS https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Sumario: | Let X be a right Hilbert C^*-module over A. We study the geometry and the topology of the projective space P(X) of X, consisting of the orthocomplemented submodules of X which are generated by a single element. We also study the geometry of the p-sphere S_p(X) and the natural fibration S_p(X) →P(X), where S_p(X)={x ∈ X : ⟨ x,x ⟩=p}, for p∈ A a projection. The projective space and the p-sphere are shown to be homogeneous differentiable spaces of the unitary group of the algebra L_A(X)$ of adjointable operators of X. The homotopy theory of these spaces is examined. |
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