A Collatz-Wielandt characterization of the spectral radius of order-preserving homogeneous maps on cones

Details A Collatz-Wielandt characterization of the spectral radius of order-preserving homogeneous maps on cones A Collatz-Wielandt characterization of the spectral radius of order-preserving homogeneous maps on cones

2011-12-27

arxiv.org/abs/1112.5968v1

Mathematics

Functional Analysis

22 pages

Scientific paper

Several notions of spectral radius arise in the study of nonlinear order-preserving positively homogeneous self-maps of cones in Banach spaces. We give conditions that guarantee that all these notions give the same value. In particular, we give a Collatz-Wielandt type formula, which characterizes the growth rate of the orbits in terms of eigenvectors in the closed cone and super-eigenvectors in the interior of the cone. This characterization holds when the cone is normal and when a quasi-compactness condition, involving an essential spectral radius defined in terms of $k$-set contractions, is satisfied.

Affiliated with

Also associated with

No associations

Rating

A Collatz-Wielandt characterization of the spectral radius of order-preserving homogeneous maps on 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 A Collatz-Wielandt characterization of the spectral radius of order-preserving homogeneous maps on cones, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Collatz-Wielandt characterization of the spectral radius of order-preserving homogeneous maps on cones will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-37298