On the Metric Compactification of Infinite Dimensional \(\ell_p\) Spaces

Dec 28, 2018·
Armando W. Gutiérrez
Armando W. Gutiérrez
· 1 min read
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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 \(\ell_p\) spaces for all \(1\leq p < \infty\). We also give a full characterization of the metric compactification of infinite dimensional Hilbert spaces.
Type
Publication
Canadian Mathematical Bulletin, 62(3), 491–507
Status
Peer-reviewed Open access
publications

Main results

Metric Functionals Metric Spaces Metric Compactification Banach Spaces Hilbert Spaces
Armando W. Gutiérrez
Authors
Armando W. Gutiérrez
Research Scientist
I’m a Researcher in Mathematics. I’ve carried out research at Aalto University, Inria Saclay, and VTT. I’ve made contributions to metric geometry, functional analysis and optimization. I’m passionate about quantum computing, risk analysis and optimization algorithms.