Projective spaces of a C*-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*-algebra A with a fixed projection p. The resulting space P(p) admits a rich geometrical structure as a holomorphic manifold and a homogeneous reductive space of the inv...
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| Autores principales: | , , |
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| Publicado: |
2000
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0378620X_v37_n2_p143_Andruchow http://hdl.handle.net/20.500.12110/paper_0378620X_v37_n2_p143_Andruchow |
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| 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*-algebra A with a fixed projection p. The resulting space P(p) admits a rich geometrical structure as a holomorphic manifold and a homogeneous reductive space of the invertible group of A. Moreover, several metrics (chordal, spherical, pseudo-chordal, non-Euclidean - in Schwarz-Zaks terminology) are considered, allowing a comparison among P(p), the Grassmann manifold of A and the space of positive elements which are unitary with respect to the bilinear form induced by the reflection ε = 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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