Abstract
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 generalization of the metric compactification that can be applied to infinite-dimensional Banach spaces. Thereafter we give a complete description of the metric compactification of infinite-dimensional $\ell_p$ spaces for all $1 \leq p < \infty$. We also give a full characterization of the metric compactification of infinite-dimensional Hilbert spaces.
Type
Publication
In Canadian Mathematical Bulletin
Armando W. Gutiérrez
Postdoctoral Researcher
Postdoctoral Researcher at Aalto University. My research interests are in metric geometry, functional analysis, optimization, and dynamics.