On the contraction properties of a pseudo-Hilbert projective metric

Maxime Ligonnière

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arXiv · 2312.11147

On the contraction properties of a pseudo-Hilbert projective metric

Maxime Ligonnière

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Abstract

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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Maxime Ligonnière. 2023-12-18. On the contraction properties of a pseudo-Hilbert projective metric. https://arxiv.org/abs/2312.11147

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