The horofunction boundary of finite-dimensional ℓp spaces

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2019
Major/Subject
Mcode
Degree programme
Language
en
Pages
15
51-65
Series
COLLOQUIUM MATHEMATICUM, Volume 155, issue 1
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 .
Description
Keywords
horofunctions, metric spaces, lp norms, variation norm, Hilbert's projective metric
Other note
Citation
Gutierrez , A W 2019 , ' The horofunction boundary of finite-dimensional ℓp spaces ' , Colloquium Mathematicum , vol. 155 , no. 1 , pp. 51-65 . https://doi.org/10.4064/cm7320-3-2018