A precision on the concept of strict convexity in non-Archimedean analysis

We prove that the only non-Archimedean strictly convex spaces are the zero space and the one-dimensional linear space over \(\, \mathbb{Z}/3\mathbb{Z}\), with any of its trivial norms.

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Bibliographic Details
Published in:arXiv.org 2021-02
Main Authors: Javier Cabello Sánchez, José Navarro Garmendia
Format: Article
Language:English
Subjects:
Convexity
Norms
Online Access:Get full text
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Description
Summary:We prove that the only non-Archimedean strictly convex spaces are the zero space and the one-dimensional linear space over \(\, \mathbb{Z}/3\mathbb{Z}\), with any of its trivial norms.
ISSN:2331-8422
DOI:10.48550/arxiv.2102.11059