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

TL;DR

This paper characterizes strictly convex spaces in non-Archimedean analysis, showing only trivial cases exist, specifically the zero space and a unique one-dimensional space over Z/3Z.

Contribution

It provides a complete classification of strictly convex spaces in non-Archimedean analysis, identifying the only such spaces as trivial or one-dimensional over Z/3Z.

Findings

Only zero space is strictly convex in non-Archimedean analysis.

A unique one-dimensional space over Z/3Z with trivial norm is strictly convex.

No other non-Archimedean spaces exhibit strict convexity.

Abstract

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.