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学者姓名：严锴
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Abstract ：
在某些算子等式成立的前提下,研究了巴拿赫空间中的Drazin可逆算子的反序律及交换关系.利用Drazin可逆算子的矩阵表示,得到了两个Drazin可逆算子的反序律成立的充分必要条件.
Keyword ：
Drazin可逆算子 Drazin可逆算子 反序律 反序律 巴拿赫空间 巴拿赫空间
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| GB/T 7714 | 曾芳莲 , 孔瑶兵 , 严锴 . 巴拿赫空间上的Drazin可逆算子的反序律 [J]. | 数学的实践与认识 , 2024 , 54 (5) : 198-206 . |
| MLA | 曾芳莲 等. "巴拿赫空间上的Drazin可逆算子的反序律" . | 数学的实践与认识 54 . 5 (2024) : 198-206 . |
| APA | 曾芳莲 , 孔瑶兵 , 严锴 . 巴拿赫空间上的Drazin可逆算子的反序律 . | 数学的实践与认识 , 2024 , 54 (5) , 198-206 . |
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Abstract ：
In this paper we find that a result of an equivalent characterization of tight K-g-frames obtained by Huang and Shi is incorrect, and we give a sufficient condition for a given Bessel sequence to be a tight K-frame. We also characterize the weaving of K-frames in Hilbert spaces. We give several kinds of sufficient conditions such that the type {T(1)f(i)}i is an element of I and {T-2gi}(i is an element of I) are K-woven (resp. woven) on H or its subspace R(K), given that {f(i)}(i is an element of I) and {g(i)}(i is an element of I) are K-frames (resp. frames) on H and T-1,T-2 are surjective operators on H. Finally we discuss that we can plus two different Bessel sequences to a K-woven pair such that the new obtained pair are K-woven on H.
Keyword ：
Frame Frame K-frame K-frame K-woven K-woven Tight Tight Weaving Weaving
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| GB/T 7714 | Xiao, Xiangchun , Yan, Kai , Zhao, Guoping et al. Tight K-frames and weaving of K-frames [J]. | JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS , 2021 , 12 (1) . |
| MLA | Xiao, Xiangchun et al. "Tight K-frames and weaving of K-frames" . | JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS 12 . 1 (2021) . |
| APA | Xiao, Xiangchun , Yan, Kai , Zhao, Guoping , Zhu, Yucan . Tight K-frames and weaving of K-frames . | JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS , 2021 , 12 (1) . |
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Abstract ：
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 et al. "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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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 et al. "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 . |
| MLA | Zeng, Qingping et al. "New results on common properties of the products AC and BA, II" . | MATHEMATISCHE NACHRICHTEN (2020) . |
| APA | Zeng, Qingping , Yan, Kai , Zhang, Shifang . New results on common properties of the products AC and BA, II . | MATHEMATISCHE NACHRICHTEN , 2020 . |
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Abstract ：
针对性质(v)和性质(gtI)的摄动稳定性问题,通过研究性质(aw)与性质(gaw)的可交换幂有限秩摄动稳定性的相关结果,同时结合性质(aw)与性质(v)、性质(gaw)与性质(gv)之间的关系,为证明性质(v)和性质(gv)在可交换幂有限秩摄动下保持稳定提供了新的方法.
Keyword ：
Weyl型定理 Weyl型定理 幂有限秩摄动 幂有限秩摄动 性质(gv) 性质(gv)
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| GB/T 7714 | 严锴 . 关于算子谱性质幂有限秩摄动的一个注记 [J]. | 福州大学学报（自然科学版） , 2020 , 48 (4) : 411-414 . |
| MLA | 严锴 . "关于算子谱性质幂有限秩摄动的一个注记" . | 福州大学学报（自然科学版） 48 . 4 (2020) : 411-414 . |
| APA | 严锴 . 关于算子谱性质幂有限秩摄动的一个注记 . | 福州大学学报（自然科学版） , 2020 , 48 (4) , 411-414 . |
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Abstract ：
In this paper, we continue to investigate common properties of the products ac and bd in various categories under the assumption acd = dbd and dba = aca. These properties include generalized strongly Drazin invertibility and generalized Hirano invertibility in rings, abstract index of Fredholm elements and B-Fredholm elements in the Banach algebra context, complementability of kernels and ranges for bounded linear operators on Banach spaces.
Keyword ：
complementability complementability generalized inverse generalized inverse index index Jacobson's lemma Jacobson's lemma
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| GB/T 7714 | Zeng, Qingping , Yan, Kai , Wu, Zhenying . FURTHER RESULTS ON COMMON PROPERTIES OF THE PRODUCTS ac AND bd [J]. | GLASNIK MATEMATICKI , 2020 , 55 (2) : 267-276 . |
| MLA | Zeng, Qingping et al. "FURTHER RESULTS ON COMMON PROPERTIES OF THE PRODUCTS ac AND bd" . | GLASNIK MATEMATICKI 55 . 2 (2020) : 267-276 . |
| APA | Zeng, Qingping , Yan, Kai , Wu, Zhenying . FURTHER RESULTS ON COMMON PROPERTIES OF THE PRODUCTS ac AND bd . | GLASNIK MATEMATICKI , 2020 , 55 (2) , 267-276 . |
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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 et al. "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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