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学者姓名：曾清平
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Abstract ：
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 the B-Fredholm resolvent set. Finally, in the context of semisimple Banach algebras, we characterize elements f such that fn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f<^>{n}$$\end{document} belongs to the socle for some n is an element of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n \in {\mathbb {N}}$$\end{document} from two different perspectives: one is the invariance of the B-Fredholm spectrum under commuting perturbation of such f, the other is f simultaneously being Riesz and B-Fredholm.
Keyword ：
Banach algebra Banach algebra B-Fredholm B-Fredholm Local spectral theory Local spectral theory Perturbation theory Perturbation theory Punctured neighbourhood theorem Punctured neighbourhood theorem Riesz Riesz Socle Socle
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| GB/T 7714 | Zhang, Yunnan , Zeng, Qingping , Wu, Zhenying . B-Fredholm theory in Banach algebras [J]. | BANACH JOURNAL OF MATHEMATICAL ANALYSIS , 2025 , 19 (4) . |
| MLA | Zhang, Yunnan 等. "B-Fredholm theory in Banach algebras" . | BANACH JOURNAL OF MATHEMATICAL ANALYSIS 19 . 4 (2025) . |
| APA | Zhang, Yunnan , Zeng, Qingping , Wu, Zhenying . B-Fredholm theory in Banach algebras . | BANACH JOURNAL OF MATHEMATICAL ANALYSIS , 2025 , 19 (4) . |
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Abstract ：
In this paper, we introduce the left (resp. right) Browder elements in a semiprime, complex and unital Banach algebra A. It is established that (i) a is an element of A is left Browder if and only if a is relatively regular and the left quasinilpotent part of a (or, the left hyperkernel of a ) is of finite order; (ii) the spectral mapping theorem holds for the left Browder spectrum; (iii) the set of all left Browder elements is an open multiplicative semigroup; (iv) the left Browder spectrum is stable under commuting Riesz perturbations; (v) Riesz elements are characterized by means of the invariance of the left Browder spectrum under commuting perturbations; (vi) the Kato decomposition for left Browder elements in primitive C* algebras is provided. Similar results hold for the right Browder elements and the right Browder spectrum. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Keyword ：
Kato decomposition Kato decomposition Left Browder element Left Browder element Perturbation Perturbation Riesz element Riesz element Right Browder element Right Browder element Spectral mapping theorem Spectral mapping theorem
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| GB/T 7714 | Wu, Zhenying , Zeng, Qingping . Left and right Browder elements in Banach algebras [J]. | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2024 , 541 (2) . |
| MLA | Wu, Zhenying 等. "Left and right Browder elements in Banach algebras" . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 541 . 2 (2024) . |
| APA | Wu, Zhenying , Zeng, Qingping . Left and right Browder elements in Banach algebras . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2024 , 541 (2) . |
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Abstract ：
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 ƒ such that ƒn belongs to the socle for some n ∈ from two different perspectives: one is the invariance of the B-Fredholm spectrum under commuting perturbation ƒ, the other is the Rieszness and the B-Fredholmness of ƒ.MSC Codes Primary 46H05, 46H10, Secondary 47A53, 47A55 Copyright © 2024, The Authors. All rights reserved.
Keyword ：
Banach spaces Banach spaces Perturbation techniques Perturbation techniques
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| GB/T 7714 | Zhang, Yunnan , Zeng, Qingping , Wu, Zhenying . B-Fredholm theory in Banach algebras [J]. | arXiv , 2024 . |
| MLA | Zhang, Yunnan 等. "B-Fredholm theory in Banach algebras" . | arXiv (2024) . |
| APA | Zhang, Yunnan , Zeng, Qingping , Wu, Zhenying . B-Fredholm theory in Banach algebras . | arXiv , 2024 . |
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It is established that the relationships between Weyl's theorem, Browder's theorem, generalized Weyl's theorem and generalized Browder's theorem in a semiprime Banach algebra A. We prove that if the commutant of a is an element of A contains a left or right injective quasinilpotent element, then f(a) satisfies Weyl's theorem for f belongs to Hol(a), the set of analytic functions on a neighborhood of sigma(a). It is shown that the accumulation points of the spectrum of an element in A are invariant under any commuting perturbation f such that F-n is an element of soc(A) for some n is an element of N. This result provides a positive answer to Question 2.8 in (Linear Multilinear Algebra 64(2):247-257, 2016), and it is then applied to investigate the perturbations of Weyl's theorem and generalized Weyl's theorem. It is also shown that if a is a hyponormal element (that is, a(& lowast;)a >= aa(& lowast;)) in a C-& lowast; algebra A and f is an element of Hol(a), then f(a) satisfies Weyl's theorem. If additionally A is primitive then f(a) obeys generalized Weyl's theorem. We also consider some other interesting properties of hyponormal elements in C* algebras, including simply polaroidness, topological divisor of zero, self-adjointness of the spectral projection with respect to lambda is an element of iso sigma(a), and the spectral mapping theorem of the Weyl spectrum.
Keyword ：
Banach algebra Banach algebra C* algebra C* algebra Generalized Weyl's theorem Generalized Weyl's theorem Hyponormal element Hyponormal element Perturbation theory Perturbation theory Weyl's theorem Weyl's theorem
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| GB/T 7714 | Wu, Zhenying , Zeng, Qingping , Zhang, Yunnan . Weyl type theorems in Banach algebras and hyponormal elements in C∗ algebras [J]. | BANACH JOURNAL OF MATHEMATICAL ANALYSIS , 2024 , 18 (2) . |
| MLA | Wu, Zhenying 等. "Weyl type theorems in Banach algebras and hyponormal elements in C∗ algebras" . | BANACH JOURNAL OF MATHEMATICAL ANALYSIS 18 . 2 (2024) . |
| APA | Wu, Zhenying , Zeng, Qingping , Zhang, Yunnan . Weyl type theorems in Banach algebras and hyponormal elements in C∗ algebras . | BANACH JOURNAL OF MATHEMATICAL ANALYSIS , 2024 , 18 (2) . |
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Abstract ：
设A是半单Banach代数，σ_D(a)表示元素a∈A的Drazin谱.证明了以下陈述等价：(i)存在n∈N使得f~n∈soc(A);(ii)σ_D(a+f)=σ_D(a),对每个与f可交换的元素a∈A.
Keyword ：
Drazin谱 Drazin谱 交换摄动 交换摄动 半单Banach代数 半单Banach代数 基座 基座
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| GB/T 7714 | 吴珍莺 , 曾清平 . Drazin谱及其交换摄动 [J]. | 福建师范大学学报(自然科学版) , 2023 , 39 (06) : 72-75 . |
| MLA | 吴珍莺 等. "Drazin谱及其交换摄动" . | 福建师范大学学报(自然科学版) 39 . 06 (2023) : 72-75 . |
| APA | 吴珍莺 , 曾清平 . Drazin谱及其交换摄动 . | 福建师范大学学报(自然科学版) , 2023 , 39 (06) , 72-75 . |
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Let a, b, c, d be elements in a unital associative ring R. In this note, we generalize Cline's formula for some new generalized inverses such as strong Drazin inverse, generalized strong Drazin inverse, Hirano inverse and generalized Hirano inverse to the case when acd = dbd and dba = aca. As a particular case, some recent results are recovered.
Keyword ：
Cline's formula Cline's formula generalized Hirano inverse generalized Hirano inverse generalized strong Drazin inverse generalized strong Drazin inverse Hirano inverse Hirano inverse ring ring strong Drazin inverse strong Drazin inverse
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| GB/T 7714 | Wu, Zhenying , Zeng, Qingping . Extensions of Cline's Formula for Some New Generalized Inverses [J]. | FILOMAT , 2021 , 35 (2) : 477-483 . |
| MLA | Wu, Zhenying 等. "Extensions of Cline's Formula for Some New Generalized Inverses" . | FILOMAT 35 . 2 (2021) : 477-483 . |
| APA | Wu, Zhenying , Zeng, Qingping . Extensions of Cline's Formula for Some New Generalized Inverses . | FILOMAT , 2021 , 35 (2) , 477-483 . |
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In this paper, new extensions of Jacobson's lemma and Cline's formula for Drazin inverses, generalized Drazin inverses, and (m, n)-pseudo-inverses are given. As applications, we provide a formula for the powers of the products of two elements and establish connections between two B-Fredholm elements through the canonical map.
Keyword ：
Cline's formula Cline's formula Drazin inverses Drazin inverses generalized Drazin inverses generalized Drazin inverses Jacobson's lemma Jacobson's lemma (m, n)-pseudo-inverses (m, n)-pseudo-inverses
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| GB/T 7714 | Yan, Kai , Zeng, Qingping . The generalized inverses of the products of two elements in a ring [J]. | TURKISH JOURNAL OF MATHEMATICS , 2020 , 44 (5) : 1744-1756 . |
| MLA | Yan, Kai 等. "The generalized inverses of the products of two elements in a ring" . | TURKISH JOURNAL OF MATHEMATICS 44 . 5 (2020) : 1744-1756 . |
| APA | Yan, Kai , Zeng, Qingping . The generalized inverses of the products of two elements in a ring . | TURKISH JOURNAL OF MATHEMATICS , 2020 , 44 (5) , 1744-1756 . |
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Let X be a Banach space and A, B, C, D be bounded linear operators on X. In this paper we show that the Drazin (resp. generalized Drazin) spectrum of AC coincides with the Drazin (resp. generalized Drazin) spectrum of BD under certain assumptions. Moreover, several interesting Banach space properties, such as SVEP and polaroidness, are considered.
Keyword ：
Drazin invertibility Drazin invertibility Generalized Drazin invertibility Generalized Drazin invertibility Operator product Operator product Spectral equation Spectral equation
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| GB/T 7714 | Yan, Kai , Zeng, Qingping , Zhu, Yucan . On Drazin Spectral Equation for the Operator Products [J]. | COMPLEX ANALYSIS AND OPERATOR THEORY , 2020 , 14 (1) . |
| MLA | Yan, Kai 等. "On Drazin Spectral Equation for the Operator Products" . | COMPLEX ANALYSIS AND OPERATOR THEORY 14 . 1 (2020) . |
| APA | Yan, Kai , Zeng, Qingping , Zhu, Yucan . On Drazin Spectral Equation for the Operator Products . | COMPLEX ANALYSIS AND OPERATOR THEORY , 2020 , 14 (1) . |
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Abstract ：
Let R be any associative ring with unit 1 and suppose that ac is Drazin (respectively, generalized Drazin, pseudo-Drazin) invertible if and only if 1-bd is Drazin (respectively, generalized Drazin, pseudo-Drazin) invertible. In other words, we give an affirmative answer to the conjecture of D. Mosic. Moreover, some applications to Banach algebra elements and Banach space operators are also given.
Keyword ：
Drazin inverse Drazin inverse generalized Drazin inverse generalized Drazin inverse Jacobson's lemma Jacobson's lemma pseudo-Drazin inverse pseudo-Drazin inverse ring ring
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| GB/T 7714 | Yan, Kai , Zeng, Qingping , Zhu, Yucan . Generalized Jacobson's lemma for Drazin inverses and its applications [J]. | LINEAR & MULTILINEAR ALGEBRA , 2020 , 68 (1) : 81-93 . |
| MLA | Yan, Kai 等. "Generalized Jacobson's lemma for Drazin inverses and its applications" . | LINEAR & MULTILINEAR ALGEBRA 68 . 1 (2020) : 81-93 . |
| APA | Yan, Kai , Zeng, Qingping , Zhu, Yucan . Generalized Jacobson's lemma for Drazin inverses and its applications . | LINEAR & MULTILINEAR ALGEBRA , 2020 , 68 (1) , 81-93 . |
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In this note, we continue to investigate common properties of the products in the setting of rings, bounded linear operators, or Banach algebras. We prove: (i) If a, b, c are elements in a unital associative ring R satisfying aba = aca, then von Neumann regularity (resp. generalized Fredholmness relative to an ideal I of R) of 1- ac is converted into that of 1- ba. (ii) If A, B, C are bounded linear operators satisfying ABA = ACA, then I - AC and I - BA share common complementability of kernels and ranges. (iii) If a, b, c are elements in a unital semisimple Banach algebra A satisfying aba = aca and I is a trace ideal of A such that soc(A) subset of I subset of kh(soc(A)), then 1- ac and 1- ba share common Fredholmness relative to I and have the same abstract index. A similar result holds for B-Fredholmness in primitive Banach algebra.
Keyword ：
Fredholm Fredholm index index kernel kernel range range von Neumann regular von Neumann regular
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| GB/T 7714 | Zeng, Qingping , Yan, Kai , Zhang, Shifang . New results on common properties of the products AC and BA, II [J]. | MATHEMATISCHE NACHRICHTEN , 2020 , 293 (8) : 1629-1635 . |
| MLA | Zeng, Qingping 等. "New results on common properties of the products AC and BA, II" . | MATHEMATISCHE NACHRICHTEN 293 . 8 (2020) : 1629-1635 . |
| APA | Zeng, Qingping , Yan, Kai , Zhang, Shifang . New results on common properties of the products AC and BA, II . | MATHEMATISCHE NACHRICHTEN , 2020 , 293 (8) , 1629-1635 . |
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