Abstract:
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.
Registro:
Documento: |
Artículo
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Título: | Projective spaces of a C*-algebra |
Autor: | Andruchow, E.; Corach, G.; Stojanoff, D. |
Filiación: | Instituto de Ciencias, UNGS, San Miguel, Argentina Depto. de Matemática, FCEN-UBA, Buenos Aires, Argentina Inst. Argentino de Matemática, Buenos Aires, Argentina Depto. de Matemática, FCE-UNLP, La Plata, Argentina
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Año: | 2000
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Volumen: | 37
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Número: | 2
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Página de inicio: | 143
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Página de fin: | 168
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DOI: |
http://dx.doi.org/10.1007/BF01192421 |
Título revista: | Integral Equations and Operator Theory
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Título revista abreviado: | Integr. Equ. Oper. Theory
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ISSN: | 0378620X
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0378620X_v37_n2_p143_Andruchow |
Referencias:
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Citas:
---------- APA ----------
Andruchow, E., Corach, G. & Stojanoff, D.
(2000)
. Projective spaces of a C*-algebra. Integral Equations and Operator Theory, 37(2), 143-168.
http://dx.doi.org/10.1007/BF01192421---------- CHICAGO ----------
Andruchow, E., Corach, G., Stojanoff, D.
"Projective spaces of a C*-algebra"
. Integral Equations and Operator Theory 37, no. 2
(2000) : 143-168.
http://dx.doi.org/10.1007/BF01192421---------- MLA ----------
Andruchow, E., Corach, G., Stojanoff, D.
"Projective spaces of a C*-algebra"
. Integral Equations and Operator Theory, vol. 37, no. 2, 2000, pp. 143-168.
http://dx.doi.org/10.1007/BF01192421---------- VANCOUVER ----------
Andruchow, E., Corach, G., Stojanoff, D. Projective spaces of a C*-algebra. Integr. Equ. Oper. Theory. 2000;37(2):143-168.
http://dx.doi.org/10.1007/BF01192421