Common Spectral Properties of Bounded Right Linear Operators AC and BA in the Quaternionic Setting

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-03-18 DOI:10.1007/s00006-024-01315-0

Rachid Arzini, Ali Jaatit

引用次数: 0

Abstract

Let X be a two-sided quaternionic Banach space and let $A, B, C: X \longrightarrow X$ be bounded right linear quaternionic operators such that $ACA=ABA$. Let q be a non-zero quaternion. In this paper, we investigate the common properties of $(AC)^{2}-2Re(q)AC+|q|^2I$ and $(BA)^{2}-2Re(q)BA+|q|^2I$ where I stands for the identity operator on X. In particular, we show that

$$\begin{aligned} \sigma ^{S}_{{\mathcal {F}}}(AC)\backslash \{0\} = \sigma ^{S}_{{\mathcal {F}}}(BA)\backslash \{0\} \end{aligned}$$

where $\sigma ^{S}_{{\mathcal {F}}}(.)$ is a distinguished part of the spherical spectrum.

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四元数背景下有界右线性算子 AC 和 BA 的共谱特性

让 X 是一个双面四元数的巴拿赫空间，并让（A, B, C: X \longrightarrow X\ ）是有界的右线性四元数算子，使得（ACA=ABA）。让 q 是一个非零四元数。本文将研究 $(AC)^{2}-2Re(q)AC+|q|^2I$ 和 $(BA)^{2}-2Re(q)BA+|q|^2I$ 的共同性质，其中 I 代表 X 上的同一算子。\sigma ^{S}_{{\mathcal {F}}(AC)\backslash \{0\} = \sigma ^{S}_{{\mathcal {F}}(BA)\backslash \{0\}\end{aligned}$$其中 $\sigma^{S}_{\mathcal {F}}(.)$ 是球谱的一个突出部分。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.