The Constants to Measure the Differences Between Isosceles and α-β Orthogonalities

Abstract

In this paper, by combining the isosceles orthogonality and α−β orthogonality of Banach spaces, we first introduce a new geometric constant. We demonstrate some basic properties about it, such as calculating its value in the common norm spaces. Moreover, the necessary and sufficient conditions for the new constant to characterize Hilbert spaces are given. Finally, only consider the points on the unit sphere, we introduce another new geometric constant and some basic properties are also obtained.