Hilbert's metric on symmetric cones

Details Hilbert's metric on symmetric cones Hilbert's metric on symmetric cones

2004-03-17

arxiv.org/abs/math/0403281v1

Mathematics

Metric Geometry

9 pages; latex

Scientific paper

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

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