Symmetric properties of orthogonality of linear operators on (Rn, ∥.∥1)

Ghosh, P and Paul, K and Sain, D (2017) Symmetric properties of orthogonality of linear operators on (Rn, ∥.∥1). In: Institute of Mathematics, 47 (2). pp. 41-46.

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Abstract

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.

Item Type:	Journal Article
Publication:	Institute of Mathematics
Publisher:	Institute of Mathematics
Additional Information:	The copyright for this article belongs to the Institute of Mathematics.
Keywords:	Birkhoff-James Orthogonality; Left symmetric operator; Right symmetric operator
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	05 Aug 2022 06:20
Last Modified:	05 Aug 2022 06:20
URI:	https://eprints.iisc.ac.in/id/eprint/74664

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