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

Ying Liu; Lining Jiang

doi:10.1515/forum-2023-0376

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

Ying Liu, Lining Jiang^*

^*此作品的通讯作者

数学学院

Beijing Institute of Technology

科研成果: 期刊稿件 › 文章 › 同行评审

1 引用（Scopus）

摘要

Let A be a complex unital Banach algebra and let R ⊂ 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 is constructed as an extension of R to axiomatically study the accumulation of σ_R(a) for any a ∈A. At last, several illustrative examples on Banach algebra and operator algebra are provided.

源语言	英语
页（从-至）	777-792
页数	16
期刊	Forum Mathematicum
卷	37
期	3
DOI	https://doi.org/10.1515/forum-2023-0376
出版状态	已接受/待刊 - 2024

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Liu, Y., & Jiang, L. (已接受/印刷中). Idempotent decomposition of regularity and characterization for the accumulation of associated spectrum. Forum Mathematicum, 37(3), 777-792. https://doi.org/10.1515/forum-2023-0376

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AB - Let A be a complex unital Banach algebra and let R ⊂ 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, RD is constructed as an extension of R to axiomatically study the accumulation of σR(a) for any a ∈A. At last, several illustrative examples on Banach algebra and operator algebra are provided.

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

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