The horofunction boundary of finite-dimensional ℓp spaces

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
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Date

2019

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Department of Mathematics and Systems Analysis

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Language

en

Pages

15

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Colloquium Mathematicum, Volume 155, issue 1, pp. 51-65

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 .

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Keywords

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

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DOI

10.4064/cm7320-3-2018

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

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https://urn.fi/URN:NBN:fi:aalto-202208104548

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[article-cris] Perustieteiden korkeakoulu / SCI