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 ℓp spaces for all 1 ≤ p < ∞. We also give a full characterization of the metric compactification of infinite-dimensional Hilbert spaces.
| Original language | English |
|---|---|
| Pages (from-to) | 491-507 |
| Journal | Canadian Mathematical Bulletin |
| Volume | 62 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Sept 2019 |
| MoE publication type | A1 Journal article-refereed |
Funding
This work was supported by the Academy of Finland, Grant No. 288318.
Keywords
- Banach space
- Horofunction compactification
- Metric compactification
- Metric functional
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