Abstract
We give a complete description of the horofunction boundary of finite-dimensional ℓ p spaces for 1 ≤ p ≤ ∞. We also study the variation norm on ℝ N , 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 ℝ N + of ℝ N .
| Original language | English |
|---|---|
| Pages (from-to) | 51-65 |
| Number of pages | 15 |
| Journal | Colloquium Mathematicum |
| Volume | 155 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2019 |
| MoE publication type | A1 Journal article-refereed |
Keywords
- horofunctions
- metric spaces
- lp norms
- variation norm
- Hilbert's projective metric