Symmetric properties of orthogonality of linear operators on (R^n, ||.||_1)
Kallol Paul, Puja Ghosh, Debmalya Sain · Novi Sad Journal of Mathematics · 2017
In this paper we study the orthogonality in the sense of Birkhoff-James of bounded linear operators on (Rn, ∥.∥1). We prove that T ⊥B A ⇒ A ⊥B T for all operators A on (Rn, ∥.∥1) if and only if T attains norm at only one extreme point, the image of which is a left symmetric point of (Rn, ∥.∥1) and images of other extreme points are zero. We also prove that A ⊥B T ⇒ T ⊥B A for all operators A on (Rn, ∥.∥1) if and only if T attains norm at all extreme points and images of the extreme points are scalar multiples of extreme points.