On height orthogonality in normed linear spaces
type: Item
instance of: scholarly article
title: On height orthogonality in normed linear spaces
zbMATH Open document ID: 0959.46004
author: Javier Alonso
author: María L. Soriano
published in: Rocky Mountain Journal of Mathematics
publication date: 2001-05-01T00:00:00Z
full work available at URL: CONT29-4.html
review text: Let \(E\) be a real normed linear space of dimension at least two. \textit{C. Alsina}, \textit{P. Guijarro} and \textit{M. S. Tomas} [Rocky Mt. J. Math. 25, No. 3, 843-849 (1995; Zbl 0845.46011)] introduced the following orthogonality: if \(x,y\in E\), then \(x\) is orthogonal to \(y\) in the height sense if either \(\|x\|\cdot\|y\|=0\) or \(\|x-y\|= \|\|y\|\cdot{x\over\|x\|}+\|x\|\cdot{y\over\|y\|}\|\). In the present paper the authors study geometric properties of \(H\)-orthogonality based on a classical property of right triangles.
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 1455464
zbMATH Keywords: orthogonality
zbMATH Keywords: geometric properties of \(H\)-orthogonality
reviewed by: Jarosław Górnicki
MaRDI profile type: Publication
OpenAlex ID: W2080339630
cites work: Area orthogonality in normed linear spaces
cites work: A characterization of inner product spaces based on orthogonal relations related to height's theorem
cites work: Characterizations of inner product spaces
cites work: Q3219302
cites work: Orthogonality in linear metric spaces
cites work: Orthogonality in normed linear spaces
cites work: Some Characterizations of Inner-Product Spaces
cites work: A New Orthogonality Relation for Normed Linear Spaces
cites work: A Remark on M. M. Day's Characterization of Inner-Product Spaces and a Conjecture of L. M. Blumenthal
DOI: 10.1216/RMJM/1181070401
description: scientific article; zbMATH DE number 1455464