Birkhoff's version of Hilbert's metric and its applications in analysis

Bas Lemmens; Roger Nussbaum

Birkhoff's version of Hilbert's metric and its applications in analysis

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1304.7921 v1 pith:HBP3YN77 submitted 2013-04-30 math.MG

Bas Lemmens , Roger Nussbaum This is my paper · ORCID

classification math.MG

keywords hilbertanalysisapplicationsmetricappeararticlebessonbirkhoff

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

read the original abstract

This is a survey article concerning applications of Hilbert's metric in the analysis and dynamics of linear and nonlinear mappings on cones. It will appear as a chapter in the "Handbook of Hilbert geometry", ed. G. Besson, A. Papadopoulos and M. Troyanov, European Mathematical Society Publishing House, Z\"urich.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Alternating minimization for computing doubly minimized Petz Renyi mutual information
quant-ph 2025-07 accept novelty 7.0 of 10

Alternating minimization provably computes the doubly minimized Petz Rényi mutual information for all quantum states, with linear convergence for α∈(1,2] and O(1/n) convergence for α∈(1/2,1).

Pith tools