2021/08/27 by Javier Cabello Sánchez, Sánchez, Javier Cabello, Francisco J. Carmona Fuertes +1
Mathematics · #Mathematical and Theoretical Analysis #advanced mathematical theories #Functional Equations Stability Results
paper · pdf · doi:10.48550/arxiv.2108.12400
Given some non-Archimedean field \mathbbK and some \mathbbK-linear space X, the usual way to define a norm over X involves the \em ultrametric inequality ‖x+y‖≤max\‖x‖,‖y‖\. In this note we will try to analyse the convenience of considering a wider variety of norms. The main result of the present note is a characterisation of the isometries between finite-dimensional linear spaces over some valued field endowed with the norm ‖ ⋅ ‖1, a result that can be seen as the closest to a Mazur--Ulam Theorem in non-Archimedean analysis.