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On the Metric Compactification of Infinite-dimensional
$\ell _{p}$ Spaces
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 62 / Issue 3 / September 2019
- Published online by Cambridge University Press:
- 28 December 2018, pp. 491-507
- Print publication:
- September 2019
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- Article
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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 
$1\leqslant p<\infty$. We also give a full characterization of the metric compactification of infinite-dimensional Hilbert spaces.
