Approximate symmetry of Birkhoff orthogonality
type: Item
instance of: scholarly article
title: Approximate symmetry of Birkhoff orthogonality
zbMATH Open document ID: 1402.46009
author: Jacek Chmieliński
author: Paweł Wójcik
published in: Journal of Mathematical Analysis and Applications
publication date: 2018-03-22T00:00:00Z
review text: The present article explores two different notions of approximate Birkhoff-James orthogonality in a normed linear space and improves some of the previously known interrelations between them. It is illustrated that there are interesting connections with the geometric properties of the normed linear space, including smoothness, strict convexity and uniform convexity. The authors introduce the notion of approximate symmetry of Birkhoff-James orthogonality and relate it with the present study. Geometric properties of the normed linear space, related to the approximate symmetry of Birkhoff-James orthogonality, are also explored in the present paper, with special emphasis on uniformly convex Banach spaces and their dual spaces. Motivated by the results obtained in these directions, the authors introduce the Birkhoff-James symmetry constant for a given Banach space that provides a quantitative measurement of how far Birkhoff-James orthogonality in the space is from being symmetric. The concepts introduced in the present paper are novel and geometrically motivated.
reviewed by: Debmalya Sain
Mathematics Subject Classification ID: 46B20
zbMATH DE Number: 6852029
zbMATH Keywords: Birkhoff orthogonality
zbMATH Keywords: approximate Birkhoff orthogonality
zbMATH Keywords: approximate symmetry of Birkhoff orthogonality
MaRDI profile type: Publication
full work available at URL: j.jmaa.2018.01.031
OpenAlex ID: W2793524711
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DOI: 10.1016/J.JMAA.2018.01.031
description: scientific article; zbMATH DE number 6852029