On the contraction properties of a pseudo-Hilbert projective metric
Résumé
In this note, we define a bounded variant on the Hilbert projective metric on an infinite dimensional space E and study the contraction properties of the projective maps associated with positive linear operators on E. More precisely, we prove that any positive linear operator acts projectively as a 1-Lipschitz map relatively to this distance. We also show that for a positive linear operator, strict projective contraction is equivalent to a property called uniform positivity.
Domaines
Analyse fonctionnelle [math.FA]| Origine | Fichiers produits par l'(les) auteur(s) |
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