On the metric compactification of infinite-dimensional ${\ell }_p$ spaces

Abstract

The notion of metric compactification was introduced by Gromov and later rediscovered by Rieffel; and 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 $1\le p<\infty$. We also give a full characterization of the metric compactification of infinite-dimensional Hilbert spaces.

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