Hilbert's metric on symmetric cones

2004/03/17 by Khalid Koufany, Koufany, Khalid
Mathematics · #FOS: Mathematics #Group Theory #Metric Geometry #Metric Geometry (math.MG) #math.MG

paper · pdf · doi:10.48550/arxiv.math/0403281

9 pages; latex

arxiv created 2004/03/17 · arxiv updated 2009/12/01

Abstract

Let Ω be a symmetric cone. In this note, we introduce the Hilbert projective metric on Ω in terms of Jordan algebras and we apply it to prove that given a linear transformation g such that g(Ω)⊂ Ω and a real number p, |p|>1, then there exists a unique element x∈Ω satisfying g(x)=x^p.

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