| Application of Hilbert＇s Projective Metric on Symmetric Cones |
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| 引用本文： | Khalid KOUFANY. Application of Hilbert＇s Projective Metric on Symmetric Cones[J]. 数学学报(英文版), 2006, 22(5): 1467-1472. DOI: 10.1007/s10114-005-0755-6 |
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| 作者姓名： | Khalid KOUFANY |
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| 作者单位： | Institut Elie Cartan, UMR 7502 （UHP-CNRS-INRIA）, Université Henri Poincard （Nancy 1）, B.P. 239, F-54506 Vandoeuvre-lès-Nancy Cedex, France |
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| 摘 要： | Let Ω be a symmetric cone. In this note, we introduce Hilbert＇s projective metric on Ω in terms of Jordan algebras and we apply it to prove that, given a linear invertible transformation g such that g（Ω） = Ω and a real number p, ｜p｜ 〉 1, there exists a unique element x ∈ Ω satisfying g（x） = x^p.
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| 关 键 词： | Hilbert投影度量 均衡锥 Jordan代数 可逆转变换 |
| 收稿时间： | 2004-01-22 |
| 修稿时间： | 2004-01-222004-09-02 |
Application of Hilbert’s Projective Metric on Symmetric Cones |
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| Khalid Koufany. Application of Hilbert’s Projective Metric on Symmetric Cones[J]. Acta Mathematica Sinica(English Series), 2006, 22(5): 1467-1472. DOI: 10.1007/s10114-005-0755-6 |
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| Authors: | Khalid Koufany |
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| Affiliation: | (1) Institut Elie Cartan, UMR 7502 (UHP–CNRS–INRIA), Université Henri Poincaré (Nancy 1), 239, F-54506 Vandoeuvre-lès-Nancy Cedex, France |
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| Abstract: | Let Ω be a symmetric cone. In this note, we introduce Hilbert’s projective metric on Ω in terms of Jordan algebras and we apply it to prove that, given a linear invertible transformation g such that g(Ω) = Ω and a real number p, |p| > 1, there exists a unique element x ∈ Ω satisfying g(x) = x p . |
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| Keywords: | Hilbert’ s projective metric Symmetric cone |
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