Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.11147 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910815614926848 |
|---|---|
| author | Ligonnière, Maxime |
| author_facet | Ligonnière, Maxime |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_11147 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the contraction properties of a pseudo-Hilbert projective metric Ligonnière, Maxime Functional Analysis 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. |
| title | On the contraction properties of a pseudo-Hilbert projective metric |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2312.11147 |