Application of Hilbert's Projective Metric on Symmetric Cones

摘要

Let Ω be a symmetric cone. In this note, we introduce Hilbert's projective metric on Ω interms of Jordan algebras and we apply it to prove that, given a linear invertible transformation g suchthat g(Ω)=Ω and a real number p,|P|>1, there exists a unique element x ∈Ω satisfying g(x)=x^p.