Characterizing the metric compactification of $L_p$ spaces by random measures

Abstract

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 represented by a random measure on a certain Polish space. By way of illustration, we revisit the $L_p$-mean ergodic theorem for $1 < p < \infty$, and Alspach’s example of an isometry on a weakly compact convex subset of $L_1$ with no fixed points.

Armando W. Gutiérrez

Postdoctoral Researcher

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