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arXiv · 1709.03462

The horofunction boundary of finite-dimensional $\ell_p$ spaces

Armando W. Gutiérrez
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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 $\mathbb{R}^{\mathcal{N}}$, $\mathcal{N}=\{1,...,N\}$, 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 $\mathbb{R}^{\mathcal{N}}$.

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Armando W. Gutiérrez. 2018-12-28. The horofunction boundary of finite-dimensional $\ell_p$ spaces. https://doi.org/10.4064/cm7320-3-2018

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