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 $1\le p\le \infty$. 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 ${\mathbb{R}}^{\mathcal{N}}$.

arXiv commentminor typos corrected

References in corpus (5)

• A maximin characterization of the escape rate of nonexpansive mappings in metrically convex spaces
• The horofunction boundary of finite-dimensional normed spaces
• Noncommutative Ergodic Theorems
• Group C*-algebras as compact quantum metric spaces
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Cited by in corpus (7)

• On the metric compactification of infinite-dimensional ${\ell }_p$ spaces
• Characterizing the metric compactification of $L_p$ spaces by random measures
• Horofunction compactifications and duality
• A metric version of Poincaré's theorem concerning biholomorphic inequivalence of domains
• Deep limits and cut-off phenomena for neural networks
• Firm non-expansive mappings in weak metric spaces
• Subinvariant metric functionals for nonexpansive mappings