A precision on the concept of strict convexity in non-Archimedean analysis. (June 2021)

• Record Type: Journal Article
• Authors: Cabello Sánchez, Javier; Navarro Garmendia, José
• Is Part Of: Nonlinear analysis. Volume 207(2021)
• Publication Date: 2021-06
• Subjects: 46S10 -- 26E30; Mazur–Ulam theorem -- Non-Archimedean normed spaces -- Strict convexity; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112304
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: We prove that the only non-Archimedean strictly convex spaces are the zero space and the one-dimensional linear space over Z ∕ 3 Z, with any of its trivial norms.