Metric Functionals and Weak Convergence
We introduce a notion of weak convergence in arbitrary metric spaces. Metric functionals are key in our analysis: weak convergence of sequences in a given metric space is tested …
Subinvariant Metric Functionals for Nonexpansive Mappings
We investigate the existence of subinvariant metric functionals for commuting families of nonexpansive mappings in noncompact subsets of Banach spaces. Our findings underscore the …
Firm non-expansive mappings in weak metric spaces
We introduce the notion of firm non-expansive mapping in weak metric spaces, extending previous work for Banach spaces and certain geodesic spaces. We prove that, for firm …
Comments on the cosmic convergence of nonexpansive maps
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 …
Characterizing the metric compactification of \(L_p\) spaces by random measures
We present a complete characterization of the metric compactification of \(L_p\) spaces for \(1\leq p < \infty\). Each element of the metric compactification of \(L_p\) is …
On the Metric Compactification of Infinite Dimensional \(\ell_p\) Spaces
The notion of metric compactification was introduced by Gromov and later rediscovered by Rieffel. It has been mainly studied on proper geodesic metric spaces. We present here a …
The Horofunction Boundary of Finite Dimensional \(\ell_p\) Spaces
We give a complete description of the horofunction boundary of finite dimensional \(\ell_p\) spaces for \(1\leq p \leq \infty\). We also study the variation norm on …