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: Andruchow, Esteban, Corach, Gustavo, Stojanoff, Demetrio
Publicado: 2000
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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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_0378620X_v37_n2_p143_Andruchow
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spelling paper:paper_0378620X_v37_n2_p143_Andruchow2023-06-08T15:40:25Z Projective spaces of a C*-algebra Andruchow, Esteban Corach, Gustavo Stojanoff, Demetrio 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. 2000 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
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection 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.
author Andruchow, Esteban
Corach, Gustavo
Stojanoff, Demetrio
spellingShingle Andruchow, Esteban
Corach, Gustavo
Stojanoff, Demetrio
Projective spaces of a C*-algebra
author_facet Andruchow, Esteban
Corach, Gustavo
Stojanoff, Demetrio
author_sort Andruchow, Esteban
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
publishDate 2000
url 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
work_keys_str_mv AT andruchowesteban projectivespacesofacalgebra
AT corachgustavo projectivespacesofacalgebra
AT stojanoffdemetrio projectivespacesofacalgebra
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