正则性的幂等分解和相关谱积累的表征

IF 17.7 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-04-24 DOI:10.1515/forum-2023-0376

Ying Liu, Li Jiang

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引用次数: 0

摘要

设𝒜 {\mathcal{A}} 是一个复单元巴纳赫代数，设 R ⊆ 𝒜 {R\subseteq\mathcal{A}} 是一个非空集。本文定义了 R 闭合幂分解的性质（简言之，（CID）性质），以探索谱分解关系。进一步，对于具有（CID）性质的上半圆性 R，构造 R D {R^{D}} 作为 R 的扩展，以公理地研究任意 a∈ 𝒜 {a\in\mathcal{A}} 的 σ R ( a ) {\sigma_{R}(a)} 的累积。 .最后，还提供了几个关于巴拿赫代数和算子代数的示例。

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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Idempotent decomposition of regularity and characterization for the accumulation of associated spectrum

Let 𝒜

{\mathcal{A}}

be a complex unital Banach algebra and let R ⊆ 𝒜

{R\subseteq\mathcal{A}}

be a non-empty set. This paper defines the property such that R is closed for idempotent decomposition (in short, (CID) property) to explore the spectral decomposition relation. Further, for an upper semiregularity R with (CID) property, R D

{R^{D}}

is constructed as an extension of R to axiomatically study the accumulation of σ R ⁢ ( a )

{\sigma_{R}(a)}

for any a ∈ 𝒜

{a\in\mathcal{A}}

. At last, several illustrative examples on Banach algebra and operator algebra are provided.

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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.