四元数背景下有界右线性算子 AC 和 BA 的共谱特性

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2024-03-18 DOI:10.1007/s00006-024-01315-0

Rachid Arzini, Ali Jaatit

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引用次数: 0

摘要

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。

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

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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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.