Banach子代数中涉及相对半紧性概念的相对本质谱的稳定性

IF 0.8 4区数学 Q2 MATHEMATICS

Filomat Pub Date : 2023-01-01 DOI:10.2298/fil2303891c

Slim Chelly

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引用次数: 0

摘要

作为作用于巴拿赫空间上的相对半紧线性算子的推广，本文提出了关于巴拿赫子代数的相对半紧元的概念。利用这一新颖的概念，我们建立了一类新的Fredholm摄动关于给定的Banach子代数B，它包含了它的非本质理想kB和[6]中建议的左Fredholm摄动集。发达的Fredholm微扰显示了B的双面封闭理想，这是表征与B相关的元素的weyl谱的关键。

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Stability of relative essential spectra involving relative demicompactness concept in Banach subalgebra

This paper develops the notion of relative demicompact elements of an algebra with respect to a Banach subalgebra as a generalization of relative demicompact linear operators acting on Banach spaces. Drawing on this novel notion, we build a new class of Fredholm perturbation regarding a given Banach subalgebra B which contains its inessential ideal kB and the set of left Fredholm perturbations suggested in [6]. The developed class of Fredholm perturbation exhibits that is a two-sided closed ideal of B that is key in the characterization of the weyl spectrum of elements affiliated with B.

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