A Mazur-Ulam theorem for Mappings of conservative distance in non-Archimedean n-normed spaces

2009/12/10 by Chu, Hahng-Yun, Ku, Se-Hyun
#46B20 #46S10 #51M25 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0912.2039

Abstract

In this article, we study the notions of n-isometries in non-Archimedean n-normed spaces over linear ordered non-Archimedean fields, and prove the Mazur-Ulam theorem in the spaces. Furthermore, we obtain some properties for n-isometries in non-Archimedean n-normed spaces.

Related

• On the concept of non-ultrametric non-Archimedean analysis
• A non-Archimedean Arens--Eells isometric embedding theorem on valued fields
• Isometries of ultrametric normed spaces
• Some topics related to metrics and norms, including ultrametrics and ultranorms
• Decompositions in direct sum of seminormed vector spaces and Mazur-Ulam theorem