Projective metrics and contraction principles for complex cones

Details Projective metrics and contraction principles for complex cones Projective metrics and contraction principles for complex cones

2008-11-18

arxiv.org/abs/0811.2930v1

Journal of the London Mathematical Society 2009; doi: 10.1112/jlms/jdp008

Mathematics

Spectral Theory

21 pages, 4 figures

Scientific paper

10.1112/jlms/jdp008

In 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.

Affiliated with

Also associated with

No associations

Rating

Projective metrics and contraction principles for complex cones does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Projective metrics and contraction principles for complex cones, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Projective metrics and contraction principles for complex cones will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-101396