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arXiv · 1802.04710

On the metric compactification of infinite-dimensional $\ell_{p}$ spaces

Armando W. Gutiérrez
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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 $1\leq p < \infty$. We also give a full characterization of the metric compactification of infinite-dimensional Hilbert spaces.

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BibTeXRIS

Armando W. Gutiérrez. 2018-02-13. On the metric compactification of infinite-dimensional $\ell_{p}$ spaces. https://doi.org/10.4153/s0008439518000681

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