A study of orthogonality of bounded linear operators

TL;DR

This paper investigates different notions of orthogonality for bounded linear operators in Hilbert and Banach spaces, introducing new concepts and exploring their properties and applications.

Contribution

It introduces a new notion of Birkhoff-James orthogonality for operators and studies its properties and relations with isosceles orthogonality in various spaces.

Findings

New notion of Birkhoff-James orthogonality introduced

Relations between orthogonality types analyzed in Banach spaces

Properties of orthogonality for positive operators and operators with disjoint support examined

Abstract

We study Birkhoff-James orthogonality and isosceles orthogonality of bounded linear operators between Hilbert spaces and Banach spaces. We explore Birkhoff-James orthogonality of bounded linear operators in light of a new notion introduced by us and also discuss some of the possible applications in this regard. We also study isosceles orthogonality of bounded (positive) linear operators on a Hilbert space and some of the related properties, including that of operators having disjoint support. We further explore the relations between Birkhoff-James orthogonality and isosceles orthogonality in a general Banach space.