Linear mappings preserving ρ-orthogonality

被引：24

作者：

Wojcik, Pawel ^{[1
]}

机构：

[1] Silesian Univ, Inst Math, PL-40007 Katowice, Poland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 386卷 / 01期

关键词：

Orthogonality in normed spaces; rho-Orthogonality; Smooth normed spaces; Orthogonality preserving linear mappings; SPACES;

D O I：

10.1016/j.jmaa.2011.07.062

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We define a rho-orthogonality in a real normed space and we consider the class of linear mappings preserving this relation. We show that a linear mapping preserving rho-orthogonality has to be a similarity, i.e., a scalar multiple of an isometry. As a result, we give a characterization of smooth spaces in terms of this orthogonality. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：171 / 176

页数：6

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