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.
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页码：171 / 176
页数：6
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