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 is an element of L(l(p)(2)) (p >= 2,p not equal infinity) is left symmetric with respect to Birkhoff-James orthogonality if and only if T is the zero operator. (C) 2016 Elsevier Inc. All rights reserved.