The differences between Birkhoff and isosceles orthogonalities in Radon planes

Abstract

The notion of orthogonality for vectors in inner product spaces is simple, interesting and fruitful. When moving to normed spaces, we have many possibilities to extend this notion. We consider Birkhoff orthogonality and isosceles orthogonality. Recently the constants which measure the difference between these orthogonalities have been investigated. The usual orthognality in inner product spaces and isosceles orthogonality in normed spaces are symmetric. However, Birkhoff orthogonality in normed spaces is not symmetric in general. A two-dimensional normed space in which Birkhoff orthogonality is symmetric is called a Radon plane. In this paper, we consider the difference between Birkhoff and isosceles orthogonalities in Radon planes.