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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0378620X_v37_n2_p143_Andruchow |
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todo:paper_0378620X_v37_n2_p143_Andruchow2023-10-03T15:33:12Z Projective spaces of a C*-algebra Andruchow, E. Corach, G. Stojanoff, D. 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. Fil:Andruchow, E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Corach, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Stojanoff, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0378620X_v37_n2_p143_Andruchow |
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Universidad de Buenos Aires |
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I-28 |
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R-134 |
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
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. |
| format |
JOUR |
| author |
Andruchow, E. Corach, G. Stojanoff, D. |
| spellingShingle |
Andruchow, E. Corach, G. Stojanoff, D. Projective spaces of a C*-algebra |
| author_facet |
Andruchow, E. Corach, G. Stojanoff, D. |
| author_sort |
Andruchow, E. |
| title |
Projective spaces of a C*-algebra |
| title_short |
Projective spaces of a C*-algebra |
| title_full |
Projective spaces of a C*-algebra |
| title_fullStr |
Projective spaces of a C*-algebra |
| title_full_unstemmed |
Projective spaces of a C*-algebra |
| title_sort |
projective spaces of a c*-algebra |
| url |
http://hdl.handle.net/20.500.12110/paper_0378620X_v37_n2_p143_Andruchow |
| work_keys_str_mv |
AT andruchowe projectivespacesofacalgebra AT corachg projectivespacesofacalgebra AT stojanoffd projectivespacesofacalgebra |
| _version_ |
1807319658173300736 |