The horofunction boundary of finite-dimensional $\ell _p$ spaces
Volume 155 / 2019
Colloquium Mathematicum 155 (2019), 51-65
MSC: Primary 51F99, 51B20, 52A21; Secondary 46B20.
DOI: 10.4064/cm7320-3-2018
Published online: 19 October 2018
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 $\mathbb R^{\mathcal {N}}$, $\mathcal N=\{1,\ldots ,N\}$, and the corresponding horofunction boundary. As a consequence, we describe the horofunctions for Hilbert’s projective metric on the interior of the standard cone $\mathbb R^{\mathcal {N}}_{+}$ of $\mathbb R^{\mathcal {N}}$.
