Orthogonality Types in Normed Linear Spaces

Javier Alonso (), Horst Martini () and Senlin Wu ()
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Javier Alonso: Instituto de Matemáticas de la Universidad de Extremadura (IMUEX)
Horst Martini: Fakultät für Mathematik, Technische Universität Chemnitz
Senlin Wu: North University of China

Chapter Chapter 4 in Surveys in Geometry I, 2022, pp 97-170 from Springer

Abstract: Abstract This chapter gives a comparing exposition of the large family of orthogonality concepts in normed linear spaces. With the help of fundamental properties that such concepts can have, or cannot have, we show their differences, similarities and direct connections. Based on this framework, we try to structurize this little subfield of the theory of real Banach spaces. For example, many characterizations of inner product spaces or of other special norm classes are presented. We also try to emphasize the geometric side of the given theoretical setting. Various open problems are posed, and a final survey can be taken as an update of the large amount of existing related literature. Hence our exposition should be useful for beginners in this research direction.

Keywords: Characterizations of ellipsoids; Characterizations of inner product spaces; Finsler geometry; Inner product spaces; Joly’s construction; Minkowski space; Normed linear space; Orthogonality in normed linear spaces; Radon curves; Zindler curves (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-86695-2_4

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DOI: 10.1007/978-3-030-86695-2_4

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