2024/12/21 by Souvik Ghosh, Kallol Paul, Ghosh, Souvik +3 · 1 citation
Computer Science · Mathematics · #Matrix Theory and Algorithms #Advanced Optimization Algorithms Research #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2412.16584
In this article we study the difference between orthogonality induced by the norm derivatives (known as ρ-orthogonality) and Birkhoff-James orthogonality in a normed linear space \mathbb X by introducing a new geometric constant, denoted by Γ(\mathbbX). We explore the relation between various geometric properties of the space and the constant Γ(\mathbbX). We also investigate the left symmetric and right symmetric elements of a normed linear space with respect to ρ-orthogonality and obtain a characterization of the same. We characterize inner product spaces among normed linear spaces using the symmetricity of ρ-orthogonality. Finally, we provide a complete description of both left symmetric and right symmetric elements with respect to ρ-orthogonality for some particular Banach spaces.