The horofunction boundary of finite-dimensional ℓp spaces

Armando W. Gutierrez*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)
34 Downloads (Pure)


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 languageEnglish
Pages (from-to)51-65
Number of pages15
JournalColloquium Mathematicum
Issue number1
Publication statusPublished - 2019
MoE publication typeA1 Journal article-refereed


  • horofunctions
  • metric spaces
  • lp norms
  • variation norm
  • Hilbert's projective metric


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