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 Z∕3Z, with any of its trivial norms.

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Bibliographic Details
Published in:Nonlinear analysis 2021-06, Vol.207, p.112304, Article 112304
Main Authors: Cabello Sánchez, Javier, Navarro Garmendia, José
Format: Article
Language:English
Subjects:
Mazur–Ulam theorem
Non-Archimedean normed spaces
Strict convexity
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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 Z∕3Z, with any of its trivial norms.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2021.112304