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

2016/07/28 by Sain, Debmalya · 2 citations
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1607.08488

Abstract

In this paper we characterize Birkhoff-James orthogonality of linear operators defined on a finite dimensional real Banach space \mathbbX. We also explore the symmetry of Birkhoff-James orthogonality of linear operators defined on \mathbbX. Using some of the related results proved in this paper, we finally prove that T ∈ \mathbbL(l_p²) (p ≥ 2, p ≠ ∞) is left symmetric with respect to Birkhoff-James orthogonality if and only if T is the zero operator. We conjecture that the result holds for any finite dimensional strictly convex and smooth real Banach space \mathbbX, in particular for the Banach spaces l_pⁿ (p > 1, p ≠ ∞).

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• On symmetricity of the norm derivatives orthogonality in operator spaces
• On preservers of strong Birkhoff-James orthogonality between C^*-algebras

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