ISOMETRY AND PHASE-ISOMETRY OF NON-ARCHIMEDEAN NORMED SPACES  

作　　者：王瑞东 姚文婷 Ruidong WANG;Wenting YAO(College of Science,Tianjin University of Technology,Tianjin 300384,China)

机构地区：[1]College of Science,Tianjin University of Technology,Tianjin 300384,China

出　　处：《Acta Mathematica Scientia》2023年第6期2377-2386,共10页数学物理学报（B辑英文版）

基　　金：supported by the Natural Science Foundation of China (12271402);the Natural Science Foundation of Tianjin City (22JCYBJC00420)。

摘　　要：In this paper,we study isometries and phase-isometries of non-Archimedean normed spaces.We show that every isometry f:Sr(X)→Sr(X),where X is a finite-dimensional non-Archimedean normed space and Sr(X)is a sphere with radius r∈||X||,is surjective if and only if is spherically complete and k is finite.Moreover,we prove that if X and Y are non-Archimedean normed spaces over non-trivially non-Archimedean valued fields with|2|=1,any phase-isometry f:X→Y is phase equivalent to an isometric operator.

关 键 词：non-Archimedean normed spaces isometry extension Wigner's theorem 

分 类 号：O177[理学—数学]