Quantitative characterization of the difference between Birkhoff orthogonality and isosceles orthogonality ✩

In this paper we introduce a new geometry constant D(X) to give a quantitative characterization of the difference between Birkhoff orthogonality and isosceles orthogonality. We show that 1 and 2(√2 − 1) is the upper and lower bound for D(X), respectively, and characterize the spaces of which D(X) attains the upper and lower bounds.We calculate D(X) when X = (R2, · p) and when X is a symmetric Minkowski plane respectively, we show that when X is a symmetric Minkowski plane D(X) = D(X∗). © 2005 Elsevier Inc. All rights reserved