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Uncovers characteristics of spectrum accumulation points in Banach algebras using R-decomposition, indicating new mathematical insights.
Let be a complex unital Banach algebra and be a regularity. In order to characterize the accumulation point of the spectrum of associated with , we define ‐decomposition of elements in , and give the conditions to make a regularity, where is the set of elements with ‐decomposition. Further, we study the relation between the spectrum of associated with and the accumulation point of the spectrum of associated with . Besides, some properties of are discussed.
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Liu et al. (2026) studied this question.
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