Aequationes mathematicae

, Volume 83, Issue 1–2, pp 153–189 | Cite as

On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces

  • Javier Alonso
  • Horst Martini
  • Senlin WuEmail author


We survey mainly recent results on the two most important orthogonality types in normed linear spaces, namely on Birkhoff orthogonality and on isosceles (or James) orthogonality. We lay special emphasis on their fundamental properties, on their differences and connections, and on geometric results and problems inspired by the respective theoretical framework. At the beginning we also present other interesting types of orthogonality. This survey can also be taken as an update of existing related representations.

Mathematics Subject Classification (2000)

46B20 46C15 52A21 


Real normed linear space Minkowski space inner product space Birkhoff orthogonality isosceles orthogonality James orthogonality bisectors Zindler curves 


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Authors and Affiliations

  1. 1.Departamento de MatemáticasUniversidad de ExtremaduraBadajozSpain
  2. 2.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany
  3. 3.Department of Applied MathematicsHarbin University of Science and TechnologyHarbinChina

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