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.
Type
Publication
Annals of Functional Analysis, 11(2), 227–243
Status
Peer-reviewed
Open access
Authors
Research Scientist
I’m a Researcher in Mathematics. I’ve carried out research at Aalto University, Inria Saclay, and VTT. I’ve made contributions to metric geometry, functional analysis and optimization. I’m passionate about quantum computing, risk analysis and optimization algorithms.