On maps that preserve orthogonality in normed spaces

被引：77

作者：

Blanco, A. ^{[1
]}

Turnsek, A.

机构：

[1] Queens Univ Belfast, Dept Pure Math, Belfast BT7 1NN, Antrim, North Ireland

[2] Univ Ljubljana, Fac Mech Engn, Ljubljana 1000, Slovenia

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2006年 / 136卷

关键词：

D O I：

10.1017/S0308210500004674

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We show that every orthogonality-preserving linear map between normed spaces is a scalar multiple of an isometry. Using this result, we generalize Uhlhorn's version of Wigner's theorem on symmetry transformations to a wide class of Banach spaces.

引用

页码：709 / 716

页数：8

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