Measurements of differences between orthogonality types

The notion of orthogonality for vectors in inner product spaces is simple, interesting and fruitful. As known, when moving to normed spaces, we have many possibilities to extend this notion in a way that the new notion of orthogonality reduces to the usual one when the norm is derived from an inner product. One of these possibilities was exploited by Roberts’ orthogonality. But, in a sense, it is too restrictive. Here we consider Birkhoff orthogonality and isosceles orthogonality, which are the most used notions of orthogonality, and study how “far” they are from orthogonality in the sense of Roberts. Related measurements of differences between pairs of orthogonality types are also studied.