论算子的近似 A-最小值和 A-数值半径正交性

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2024-06-25 DOI:10.1007/s10474-024-01439-6

C. Conde, K. Feki

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引用次数: 0

摘要

本文以半希尔伯特空间上的算子为背景，探讨了近似伯克霍夫-詹姆斯正交性的概念。这些空间由正半定倍线性形式生成。我们深入探讨了这一概念的基本性质，并提供了若干特征。利用创新论证，我们扩展了最初由 Magajna [17] 提出的一个广为人知的结果。此外，我们还改进了 Sen 和 Paul [24] 最近关于两个半希尔伯特空间算子近似数值半径正交性的一个结果，即其中一个算子是 \(A\)-positive 的。这里，\(A\)被假定为正半有限算子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On approximate A-seminorm and A-numerical radius orthogonality of operators

This paper explores the concept of approximate Birkhoff–James orthogonality in the context of operators on semi-Hilbert spaces. These spaces are generated by positive semi-definite sesquilinear forms. We delve into the fundamental properties of this concept and provide several characterizations of it. Using innovative arguments, we extend a widely known result initially proposed by Magajna [17]. Additionally, we improve a recent result by Sen and Paul [24] regarding a characterization of approximate numerical radius orthogonality of two semi-Hilbert space operators, such that one of them is \(A\)-positive. Here, \(A\) is assumed to be a positive semi-definite operator.

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.