The horofunction boundary of finite-dimensional $\ell_{p}$ spaces

Abstract

We give a complete description of the horofunction boundary of finite-dimensional $\ell_{p}$ spaces for $1 \leq p \leq \infty$. We also study the variation norm on $\mathbf{R}^\mathcal{N}$, $\mathcal{N}=\{1,…,N\}$, and the corresponding horofunction boundary. As a consequence, we describe the horofunctions for Hilbert’s projective metric on the interior of the standard cone $\mathbf{R}^\mathcal{N}_{+}$ of $\mathbf{R}^\mathcal{N}$.

Armando W. Gutiérrez

Postdoctoral Researcher

Postdoctoral Researcher at Aalto University. My research interests are in metric geometry, functional analysis, optimization, and dynamics.