[3] Instituto Argentino de Matemática,Depto. de Matemática
[4] FCE-UNLP,undefined
[5] Instituto Argentino de Matemática,undefined
来源:
Integral Equations and Operator Theory
|
2000年
/
37卷
关键词:
Primary 46L05, 58B20;
D O I:
暂无
中图分类号:
学科分类号:
摘要:
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 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.
机构:
Institut für Geometrie, Technische Universität, Wiedner Hauptstraβe 8–10, WienInstitut für Geometrie, Technische Universität, Wiedner Hauptstraβe 8–10, Wien
Blunck A.
Havlicek H.
论文数: 0引用数: 0
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机构:
Institut für Geometrie, Technische Universität, Wiedner Hauptstraβe 8–10, WienInstitut für Geometrie, Technische Universität, Wiedner Hauptstraβe 8–10, Wien