Projective metrics and contraction principles for complex cones

Simple item page
dc.creatorDubois, Loic
dc.date2008-11-18
dc.date.accessioned2026-07-07T13:06:12Z
dc.date.available2026-07-07T13:06:12Z
dc.descriptionIn this article, we consider linearly convex complex cones in complex Banach spaces and we define a new projective metric on these cones. Compared to the hyperbolic gauge of Rugh, it has the advantage of being explicit, and easier to estimate. We prove that this metric also satisfies a contraction principle like Birkhoff's theorem for the Hilbert metric. We are thus able to improve existing results on spectral gaps for complex matrices. Finally, we compare the contraction principles for the hyperbolic gauge and our metric on particular cones, including complexification of Birkhoff cones. It appears that the contraction principles for our metric and the hyperbolic gauge occur simultaneously on these cones. However, we get better contraction rates with our metric.
dc.description21 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/0811.2930
dc.identifierhttp://arxiv.org/abs/0811.2930
dc.identifierJournal of the London Mathematical Society 2009; doi: 10.1112/jlms/jdp008
dc.identifierdoi:10.1112/jlms/jdp008
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227706
dc.subjectSpectral Theory
dc.subjectDynamical Systems
dc.subject15A48, 47A75, 47B65
dc.titleProjective metrics and contraction principles for complex cones
dc.typetext

Files

Collections

arXiv