This is an announcement for the paper “On the metric compactification of infinite-dimensional Banach spaces” by Armando W. Gutiérrezhttps://arxiv.org/find/math/1/au:+Gutierrez_A/0/1/0/all/0/1.
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.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1802.04710