The horofunction boundary of finite-dimensional 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}}.
