TY - JOUR
T1 - The horofunction boundary of finite-dimensional ℓ p spaces
AU - Gutiérrez, Armando W.
N1 - Publisher Copyright:
© Instytut Matematyczny PAN, 2019.
PY - 2019
Y1 - 2019
N2 - 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 .
AB - 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 .
KW - Hilbert’s projective metric
KW - horofunction
KW - metric spaces
KW - variation norm
KW - positive cone
UR - https://arxiv.org/abs/1709.03462
UR - https://zbmath.org/1415.51015
UR - https://www.scopus.com/pages/publications/85062390403
U2 - 10.4064/cm7320-3-2018
DO - 10.4064/cm7320-3-2018
M3 - Article
AN - SCOPUS:85062390403
SN - 0010-1354
VL - 155
SP - 51
EP - 65
JO - Colloquium Mathematicum
JF - Colloquium Mathematicum
IS - 1
ER -