Projective spaces of a <i>C*</i>-algebra
Based on the projective matrix spaces studied by B. Schwarz and A. Zaks, we study the notion of projective space associated to a C*-algebraA with a fixed projectionp. The resulting spaceP(p) admits a rich geometrical structure as a holomorphic manifold and a homogeneous reductive space of the invert...
Guardado en:
| Autores principales: | , , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
| Publicado: |
2000
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/137455 |
| Aporte de: |
| Sumario: | Based on the projective matrix spaces studied by B. Schwarz and A. Zaks, we study the notion of projective space associated to a C*-algebraA with a fixed projectionp. The resulting spaceP(p) admits a rich geometrical structure as a holomorphic manifold and a homogeneous reductive space of the invertible group ofA. Moreover, several metrics (chordal, spherical, pseudo-chordal, non-Euclidean-in Schwarz-Zaks terminology) are considered, allowing a comparison amongP(p), the Grassmann manifold ofA and the space of positive elements which are unitary with respect to the bilinear form induced by the reflection e=2p−1. Among several metrical results, we prove that geodesics are unique and of minimal length when measured with the spherical and non-Euclidean metrics. |
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