Phase-isometries between normed spaces

被引：18

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

页码：99 / 111

页数：13

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