Symmetric properties of orthogonality of linear operators on (R^n, ||.||_1)

Puja Ghosh ; Kallol Paul  ; Debmalya Sain

Novi Sad Journal of Mathematics, Tome 47 (2017) no. 2.

Résumé

In this paper we study the orthogonality in the sense of Birkhoff-James of bounded linear operators on $ (\mathbb{R}^n, \|.\|_{1}).$ We prove that $T\perp_B A \Rightarrow A\perp_B T$ for all operators $A$ on $(\mathbb{R}^n, \|.\|_1 )$ if and only if $T$ attains norm at only one extreme point, image of which is a left symmetric point of $(\mathbb{R}^n, \|.\|_1)$ and images of other extreme points are zero. We also prove that $A\perp_B T \Rightarrow T\perp_B A$ for all operators $A$ on $(\mathbb{R}^n, \|.\|_1 )$ if and only if $T$ attains norm at all extreme points and images of the extreme points are scalar multiples of extreme points.

Détail

Publié le : 2017-06-10

DOI : 10.30755/NSJOM.04671

Classification : 47A30, 47A99
Keywords: Birkhoff-James Orthogonality, left symmetric operator, right symmetric operator