近似正交性及其在特定类别线性算子中的应用

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2025-05-08 DOI:10.1016/j.bulsci.2025.103645

Najla Altwaijry , Jacek Chmieliński , Cristian Conde , Kais Feki

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引用次数: 0

摘要

本文给出赋范空间中近似Birkhoff-James正交的新结果。主要通过推广范数导数的思想，在一般复赋范线性空间中建立了这一概念的一个表征。此外，我们在Hilbert空间中的有界线性算子的背景下研究和表征了这种类型的正交性，特别关注那些接近紧算子的理想和那些属于p-Schatten类的算子。

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Approximate orthogonality and its applications to specific classes of linear operators

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.

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