Comments on the cosmic convergence of nonexpansive maps

Abstract

This note discusses some aspects of the asymptotic behaviour of nonexpansive maps. Using metric functionals, we make a connection to the invariant subspace problem and prove a new result for nonexpansive maps of $\ell_{1}$. We also point out some inaccurate assertions appearing in the literature on this topic.

Armando W. Gutiérrez

Postdoctoral Researcher

Postdoctoral Researcher at Aalto University. My research interests are in metric geometry, functional analysis, optimization, and dynamics.