Phase-isometries between normed spaces

被引：20
作者：
Ilisevic, Dijana [1 ]
Omladic, Matjaz [2 ]
Turnsek, Aleksej [2 ,3 ]
机构：
[1] Univ Zagreb, Fac Sci, Dept Math, Zagreb, Croatia
[2] Inst Math Phys & Mech, Jadranska 19, Ljubljana 1000, Slovenia
[3] Univ Ljubljana, Fac Maritime Studies & Transport, Pot Pomorscakov 4, Portoroz 6320, Slovenia
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2021年 / 612卷
关键词：
Phase-isometry; Wigner's theorem; Isometry; Real normed space; Projective geometry; WIGNERS THEOREM; ELEMENTARY PROOF; ORTHOGONALITY;
D O I：
10.1016/j.laa.2020.12.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let X and Y be real normed spaces and f : X -> Y a surjective mapping. Then f satisfies {parallel to f (x) + f (y)parallel to, parallel to f (x) - f(y)parallel to} = {parallel to x + y parallel to, parallel to x - y parallel to}, x,y is an element of X, if and only if f is phase equivalent to a surjective linear isometry, that is, f = sigma U, where U: X -> Y is a surjective linear isometry and sigma: X -> {-1, 1}. This is a Wigner's type result for real normed spaces. (C) 2020 Elsevier Inc. All rights reserved.
引用
收藏
页码：99 / 111
页数：13
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