Approximate orthogonality and its applications to specific classes of linear operators

Abstract

This paper presents new results on approximate Birkhoff–James orthogonality in normed spaces. Mainly, by extending the idea of norm derivatives, we establish a characterization of this concept in general complex normed linear spaces. Additionally, we investigate and characterize this type of orthogonality in the context of bounded linear operators in Hilbert spaces, with a particular focus on operators that are close to the ideal of compact operators and those that belong to the p-Schatten class.