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 characterizationof 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.