Orthogonalities, linear operators, and characterization of inner product spaces
type: Item
instance of: scholarly article
title: Orthogonalities, linear operators, and characterization of inner product spaces
zbMATH Open document ID: 1390.46014
author: Senlin Wu
author: Chan He
author: Guang Yang
published in: Aequationes Mathematicae
publication date: 2017-10-26T00:00:00Z
review text: The paper under review explores the reversion of Birkhoff orthogonality under a bounded linear operator between real Banach spaces. Among other things, the authors obtain an interesting characterization of inner product spaces of dimension greater than or equal to \(3\), in terms of the existence of a bounded linear operator reversing Birkhoff orthogonality. The paper also relates isosceles orthogonality and Birkhoff orthogonality via a bounded linear operator, and the authors obtain some further characterizations of inner product spaces of dimension greater than or equal to \(3\). Furthermore, the connection between superior (inferior) semi-inner-products and Birkhoff orthogonality is explored to obtain a sufficient condition for a two-dimensional smooth Banach space to be a Radon plane. In the view of this reviewer, this is an interesting mathematical work that appeals to anyone interested in the study of various notions of orthogonality, or, in a broader sense, understanding the geometry of Banach spaces through orthogonality and bounded linear operators.
reviewed by: Debmalya Sain
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 46C15
Mathematics Subject Classification ID: 15A86
zbMATH DE Number: 6798721
zbMATH Keywords: Birkhoff orthogonality
zbMATH Keywords: isosceles orthogonality
zbMATH Keywords: characterization of inner product spaces
zbMATH Keywords: orthogonality reversing operators
MaRDI profile type: Publication
full work available at URL: s00010-017-0494-7
OpenAlex ID: W2619529296
cites work: On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces
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cites work: Two mappings related to semi-inner products and their applications in geometry of normed linear spaces
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cites work: Q3542719
cites work: Operators Reversing Orthogonality and Characterization of Inner Product Spaces
DOI: 10.1007/S00010-017-0494-7
description: scientific article; zbMATH DE number 6798721