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^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	777-792
Number of pages	16
Journal	Forum Mathematicum
Volume	37
Issue number	3
DOIs	https://doi.org/10.1515/forum-2023-0376
Publication status	Published - 1 May 2025

Keywords

Banach algebra
Idempotent decomposition
regularity
spectrum

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abstract = "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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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.

KW - Banach algebra

KW - Idempotent decomposition

KW - regularity

KW - spectrum

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

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