mean ergodic theorem

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.

We present a complete characterization of the metric compactification of $L_p$ spaces for $1 \\leq p