On Linear Operators that Preserve BJ-Orthogonality in 2-Normed Spaces

被引：0

作者：

Iranmanesh, M. ^{[1
]}

Sanatee, A. Ganjbakhsh ^{[2
]}

机构：

[1] Shahroud Univ Technol, Math, Dept Math, Shahrood, Iran

[2] Quchan Univ Technol, Dept Math, Math, Quchan, Iran

来源：

JOURNAL OF MATHEMATICAL EXTENSION | 2021年 / 15卷 / 01期

关键词：

2-Normed space; Birkhoff-James orthogo-nality; 2-Banach space; 2-isometry;

D O I：

10.30495/JME.2021.1269

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let X be a real 2-Banach space. We follow Gunawan, Mashadi, Gemawati, Nursupiamin and Siwaningrum in saying that x is orthogonal to y if there exists a subspace V of X with codim(V) = 1 such that parallel to x +lambda y,z parallel to >= parallel to x,z parallel to for every z is an element of V and lambda is an element of R. In this paper, we prove that every linear mapping T : X -> X which preserve orthogonality is a 2-isometry multiplied by a constant.

引用

页码：29 / 40

页数：12

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