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 $1\le p<\infty$. 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.

Minor corrections. Title was modified. Main results and their proofs remain unchanged. To appear in Annals of Functional Analysis

References in corpus (3)

• The horofunction boundary of finite-dimensional ${\ell }_p$ spaces
• The skeleton of the UIPT, seen from infinity
• Elements of a metric spectral theory

Cited by in corpus (4)

• Horofunction compactifications and duality
• Horofunction compactifications of symmetric cones under Finsler distances
• Deep limits and cut-off phenomena for neural networks
• Firm non-expansive mappings in weak metric spaces