Birkhoff-James orthogonality of linear operators on finite dimensional Banach spaces

In this paper we characterize Birkhoff-James orthogonality of linear operators defined on a finite dimensional real Banach space X. We also explore the left symmetry of Birkhoff-James orthogonality of linear operators defined on X. Using some of the related results proved in this paper, we finally prove that T∈L(lp2) (p≥2,p≠∞) is left symmetric with respect to Birkhoff-James orthogonality if and only if T is the zero operator.