2024/02/01 by Yunnan Zhang, Zhang, Yunnan, Qingping Zeng +3
Mathematics · #46H10 #47A55 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Primary 46H05 #Secondary 47A53
paper · pdf · doi:10.48550/arxiv.2402.00574
openalex publication_date 2024/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to develop a systematic B-Fredholm theory in semiprime Banach algebras. We first generalize Smyth's important punctured neighbourhood theorem to B-Fredholm elements. Then using this result, we investigate the local spectral theory of B-Fredholm elements, including the localized left (resp. right) SVEP and a classification of components of B-Fredholm resolvent set. Finally, in semisimple Banach algebra context, we characterize element f such that fn belongs to the socle for some n ∈ ℕ from two different perspectives: one is the invariance of the B-Fredholm spectrum under commuting perturbation f, the other is the Rieszness and the B-Fredholmness of f.