A Mazur--Ulam theorem in non-Archimedean normed spaces
Functional Analysis
2021-07-23 v1 Classical Analysis and ODEs
Abstract
The classical Mazur--Ulam theorem which states that every surjective isometry between real normed spaces is affine is not valid for non-Archimedean normed spaces. In this paper, we establish a Mazur--Ulam theorem in the non-Archimedean strictly convex normed spaces.
Cite
@article{arxiv.0710.0107,
title = {A Mazur--Ulam theorem in non-Archimedean normed spaces},
author = {Mohammad Sal Moslehian and Ghadir Sadeghi},
journal= {arXiv preprint arXiv:0710.0107},
year = {2021}
}
Comments
5 pages, to appear in Nonlinear Analysis: Theory, Methods & Applications