Orthogonalities, linear operators, and characterization of inner product spaces

被引：2

作者：

Wu, Senlin ^{[1
]}

He, Chan ^{[1
]}

Yang, Guang ^{[1
]}

机构：

[1] Harbin Univ Sci & Technol, Dept Appl Math, Harbin 150080, Heilongjiang, Peoples R China

来源：

AEQUATIONES MATHEMATICAE | 2017年 / 91卷 / 05期

关键词：

Birkhoff orthogonality; Isosceles orthogonality; Characterization of inner product spaces; Orthogonality reversing operators;

D O I：

10.1007/s00010-017-0494-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

It is proved that a normed space, whose dimension is at least three, admitting a nonzero linear operator reversing Birkhoff orthogonality is an inner product space, which releases the smoothness condition in one of J. ChmieliA"ski's results. Further characterizations of inner product spaces are obtained by studying properties of linear operators related to Birkhoff orthogonality and isosceles orthogonality.

引用

页码：969 / 978

页数：10

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