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

Abstract

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.