Pré-Publication, Document De Travail Année : 2023

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.
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Dates et versions

hal-04355849 , version 1 (20-12-2023)
hal-04355849 , version 2 (06-02-2025)

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Maxime Ligonnière. On the contraction properties of a pseudo-Hilbert projective metric. 2023. ⟨hal-04355849v2⟩
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