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The James constant in Radon planes

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Abstract

To describe the geometry of normed spaces, many geometric constants have been investigated. Among them, the James constant has been treated by a lot of mathematicians. Here we also consider Birkhoff orthogonality and isosceles orthogonality. The usual orthogonality in inner product spaces and isosceles orthogonality in normed spaces are symmetric. However, Birkhoff orthogonality is not symmetric in general normed spaces. A two-dimensional normed space in which Birkhoff orthogonality is symmetric is called Radon plane. We consider the values of James constants in Radon planes.

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Correspondence to Hiroyasu Mizuguchi.

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Mizuguchi, H. The James constant in Radon planes. Aequat. Math. (2020). https://doi.org/10.1007/s00010-020-00698-2

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Keywords

  • James constant
  • Birkhoff orthogonality
  • Isosceles orthogonality
  • Sine function
  • Radon plane
  • Minkowski plane

Mathematics Subject Classification

  • 46B20
  • 51B20
  • 52A21