2024/09/19 by Divya Khurana, Khurana, Divya
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2409.12546
openalex publication_date 2024/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
We study approximately orthogonality (in the sense of Dragomir) preserving and reversing operators. We show that for some orthogonality notations, an operator defined from a finite-dimensional Banach space to a normed linear space is approximately orthogonality preserving/reversing if and only if it is an injective operator. This result implies that for some orthogonality notations, any operator defined from an n-dimensional Banach space to another n-dimensional Banach space is approximately orthogonality preserving/reversing if and only if it is a scalar multiple of an ε-isometry. We show that any ε-isometry and maps close to ε-isometries defined from a normed linear space to another normed linear space are approximately orthogonality preserving/reversing for some orthogonality notations. We also study the locally approximate orthogonality preserving and reversing operators defined on some finite-dimensional Banach spaces.