Geometric constants for quantifying the difference between orthogonality types

V. Balestro, H. Martini and R. Teixeira, Geometric constants for quantifying the difference between orthogonality types, Annals of Functional Analysis 7(4), pp. 656-671, 2016. (arXiv link) (journal link)

Comments: In a normed plane, Roberts orthogonality is closely related to bisectors of two points which are straight lines. Using this fact, we could define a geometric constant which measures how far these bisectors are from being straight lines, and this measures how far are Birkhoff and Roberts orthogonality types. Roberts orthogonality is also related to certain symmetries of the unit circle, and this approach leads to a new geometric constant which measures the difference between the referred orthogonality types by regarding the maximum “distortion” in the unit circle with respect to such symmetries. For these constants we derive inequalities, calculate examples, and the extremal cases of both constants are also characterized.