A conjectured class of scale-invariant distances on inner product spaces

2014/01/07 by Bruno Galvan, Galvan, Bruno
Mathematics · Physics and Astronomy · #Advanced Banach Space Theory #Analytic and geometric function theory #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #math-ph #math.FA #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.1401.1524

This paper has been withdrawn by the author. The conjecture was already been made and solved. See Peter A. Hästö, A new weighted metric: the relative metric I, J. Math. Anal. Appl. 274, 38-58 (2002). Thanks to prof. Heinz Bauschke

openalex publication_date 2014/01/07 · arxiv created 2014/01/09 · arxiv updated 2014/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let V be an inner product space, and x, y ∈ V; the conjecture is made that, for any p ∈ [1, ∞], the function d_p(x, y):=‖x-y‖/(‖x‖^p+ ‖y‖^p)^1/p is a distance on V.

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