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学者姓名：林丽琼
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Abstract ：
本文首先给出Banach空间上闭强不可约算子的定义,并给出一个无界强不可约算子的例子;其次给出闭强不可约算子的性质,特别地,给出了闭强不可约算子的一些等价描述;最后给出上三角算子矩阵表示的闭算子具有强不可约性的一些充分条件.
Keyword ：
Banach空间 Banach空间 强不可约算子 强不可约算子 闭算子 闭算子
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| GB/T 7714 | 林丽琼 , 阙佳华 , 张云南 . Banach空间上的闭强不可约算子 [J]. | 数学学报 , 2023 , 66 (2) : 209-222 . |
| MLA | 林丽琼 等. "Banach空间上的闭强不可约算子" . | 数学学报 66 . 2 (2023) : 209-222 . |
| APA | 林丽琼 , 阙佳华 , 张云南 . Banach空间上的闭强不可约算子 . | 数学学报 , 2023 , 66 (2) , 209-222 . |
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本文说明Banach空间上p-fusion框架和p-框架有紧密联系.应用分析算子和合成算子给出p-fusion Bessel序列、p-fusion框架和q-fusion Riesz基的等价描述.
Keyword ：
Banach空间 Banach空间 p-fusion框架 p-fusion框架 q-fusion Riesz基 q-fusion Riesz基
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| GB/T 7714 | 林丽琼 , 张云南 . Banach空间上p-fusion框架的若干等价描述 [J]. | 数学学报(中文版) , 2021 , 64 (02) : 301-310 . |
| MLA | 林丽琼 等. "Banach空间上p-fusion框架的若干等价描述" . | 数学学报(中文版) 64 . 02 (2021) : 301-310 . |
| APA | 林丽琼 , 张云南 . Banach空间上p-fusion框架的若干等价描述 . | 数学学报(中文版) , 2021 , 64 (02) , 301-310 . |
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无穷小等价替换是计算极限一种常用且好用的方法,但要求替换项在极限点的某个邻域内没有零点,文章证明了函数在极限点的任意邻域都出现零点时,满足一定条件,等价替换仍可实施.另外利用极坐标计算二元函数极限时有诸多的限制,文章针对一类特殊函数给出了应用极坐标便于计算应用的若干结论.
Keyword ：
无穷小 无穷小 极坐标 极坐标 极限 极限 等价替换 等价替换
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| GB/T 7714 | 周燕 , 林丽琼 , 任立英 . 关于求解极限的若干思考 [J]. | 大学数学 , 2021 , 37 (2) : 108-113 . |
| MLA | 周燕 等. "关于求解极限的若干思考" . | 大学数学 37 . 2 (2021) : 108-113 . |
| APA | 周燕 , 林丽琼 , 任立英 . 关于求解极限的若干思考 . | 大学数学 , 2021 , 37 (2) , 108-113 . |
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作为Hilbert空间上编排框架和编排Riesz基的推广,本文研究Banach空间上编排p-框架和编排q-Riesz基.两个p-框架{x*n}∞n=1和{y*n}∞n=1称为是可编排的,如果存在常数0＜A≤B＜+∞,使得对N的任意子集σ,序列{x*n}n∈σ∪{y*n}n∈σc是一个p-框架且有p-框架界A和B.每个序列{x*n}n∈σ∪{y*n}n∈σc称为一个编排.可编排的q-Riesz基具有类似的定义.本文证明Banach空间上的两个-框架是可编排的当且仅当它们的每个编排是个p-框架,考虑对偶空间中两个q-Riesz基的可编排性,即借助q-Riesz序列和p-框架的性质给出两个q-Riesz基的每个编排均是q-Riesz基的条件,借助子空间距离的概念给出两个q-Riesz基可编排的几何特征.此外,本文还考虑编排p-框架和编排q-Riesz基的摄动,如小摄动和算子摄动.
Keyword ：
p-框架 p-框架 q-Riesz基 q-Riesz基 子空间距离 子空间距离 摄动 摄动
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| GB/T 7714 | 林丽琼 , 张云南 , 周燕 . 编排p-框架和编排q-Riesz基 [J]. | 中国科学（数学） , 2018 , 48 (4) : 519-530 . |
| MLA | 林丽琼 等. "编排p-框架和编排q-Riesz基" . | 中国科学（数学） 48 . 4 (2018) : 519-530 . |
| APA | 林丽琼 , 张云南 , 周燕 . 编排p-框架和编排q-Riesz基 . | 中国科学（数学） , 2018 , 48 (4) , 519-530 . |
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Abstract ：
In the research of frame theory, the questions that what kinds of invertible operators can make some frame properties remain unchanged are essential and important. This paper study the following two questions on infinite dimensional Hilbert spaces. Question one: what kind of invertible operators can make the frame operators remain unchanged; Question two: what kind of invertible operators can makes the norms of frames are a multiple by a fixed sequence of the norms of original frames. This paper gives the answer of Question one by the abstract operator theory and by the concrete constructions. When limited the class of invertible operators to a smaller class of operators, this paper obtain the answer of Question two by using the concept of admissible operators of frames. © 2017, Chinese Academy of Sciences. All right reserved.
Keyword ：
Frame; Frame operator; Hilbert space; Norm Frame; Frame operator; Hilbert space; Norm
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| GB/T 7714 | Lin, L.Q. , Zhang, Y.N. , Zhu, Y.C. . Operators and Norms of Frames on Infinite-Dimensional Hilbert Spaces [J]. | Acta Mathematica Sinica, Chinese Series , 2017 , 60 (6) : 911-918 . |
| MLA | Lin, L.Q. 等. "Operators and Norms of Frames on Infinite-Dimensional Hilbert Spaces" . | Acta Mathematica Sinica, Chinese Series 60 . 6 (2017) : 911-918 . |
| APA | Lin, L.Q. , Zhang, Y.N. , Zhu, Y.C. . Operators and Norms of Frames on Infinite-Dimensional Hilbert Spaces . | Acta Mathematica Sinica, Chinese Series , 2017 , 60 (6) , 911-918 . |
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鉴于Banach空间上的框架没有合适的框架算子定义,本文考虑Banach空间上满足一定条件的一类序列,把它称为σ-框架,并相应于这类序列给出σ-框架算子的概念.σ-框架及其σ-框架算子是Hilbert空间上框架及其框架算子的自然推广.本文说明σ-框架算子是正的、自共轭的、可通过l2分解的,并得到σ-框架在算子摄动下的结果.本文还说明σ-框架包含Banach空间上的另外两类框架-p-框架(1＜p≤2)和σHS(σHilbert-Schauder)框架,其中σHS是根据HS (Hilbert-Schauder)框架的定义而引入的一类框架,最后还得到了p框架(1＜p≤2)和σHS框架在算子摄动下的结果.
Keyword ：
Banach空间 Banach空间 Hilbert-Schauder框架 Hilbert-Schauder框架 p-框架 p-框架 σ-框架算子 σ-框架算子
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| GB/T 7714 | 林丽琼 , 张云南 , 朱玉灿 . p-框架、Hilbert-Schauder框架与σ-框架算子 [J]. | 中国科学（数学） , 2016 , 46 (12) : 1791-1800 . |
| MLA | 林丽琼 等. "p-框架、Hilbert-Schauder框架与σ-框架算子" . | 中国科学（数学） 46 . 12 (2016) : 1791-1800 . |
| APA | 林丽琼 , 张云南 , 朱玉灿 . p-框架、Hilbert-Schauder框架与σ-框架算子 . | 中国科学（数学） , 2016 , 46 (12) , 1791-1800 . |
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Let B-n(Omega) be the set of Cowen-Douglas operators of index n on a nonempty bounded connected open subset Omega of C. We consider the strong irreducibility of a class of Cowen-Douglas operators F B-n(Omega) on Banach spaces. We show F B-n(Omega) subset of B-n(Omega) and give some conditions under which an operator T is an element of F B-n(Omega) is strongly irreducible. All these results generalise similar results on Hilbert spaces.
Keyword ：
Banach spaces Banach spaces Cowen-Douglas operators Cowen-Douglas operators Rosenblum operators Rosenblum operators strongly irreducible operators strongly irreducible operators
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| GB/T 7714 | Lin, Liqiong , Zhang, Yunnan . THE STRONG IRREDUCIBILITY OF A CLASS OF COWEN-DOUGLAS OPERATORS ON BANACH SPACES [J]. | BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY , 2016 , 94 (3) : 479-488 . |
| MLA | Lin, Liqiong 等. "THE STRONG IRREDUCIBILITY OF A CLASS OF COWEN-DOUGLAS OPERATORS ON BANACH SPACES" . | BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY 94 . 3 (2016) : 479-488 . |
| APA | Lin, Liqiong , Zhang, Yunnan . THE STRONG IRREDUCIBILITY OF A CLASS OF COWEN-DOUGLAS OPERATORS ON BANACH SPACES . | BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY , 2016 , 94 (3) , 479-488 . |
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This paper gives the concepts of finite dimensional irreducible operators ((FDI) operators) and infinite dimensional irreducible operators ((IDI) operators). Discusses the relationships of (FDI) operators, (IDI) operators and strongly irreducible operators ((SI) operators) and illustrates some properties of the three classes of operators. Some sufficient conditions for the finite-dimensional irreducibility of operators which have the forms of upper triangular operator matrices are given. This paper proves that every operator with a singleton spectrum is a small compact perturbation of an (FDI) operator on separable Banach spaces and shows that every bounded linear operator T can be approximated by operators in (I FDI)(X) pound with respect to the strong-operator topology and every compact operator K can be approximated by operators in (I FDI)(X) pound with respect to the norm topology on a Banach space X with a Schauder basis, where (I FDI)(X) pound:= {T a B(X): T = I pound (i=1) (k) aS center dot T (i) , T (i) a (FDI), k is an element of N}.
Keyword ：
Banach spaces Banach spaces operators with irreducibility operators with irreducibility small and compact perturbations small and compact perturbations strongly irreducible operators strongly irreducible operators
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| GB/T 7714 | Zhang, Yun Nan , Lin, Li Qiong . Two classes of operators with irreducibility and the small and compact perturbations of them [J]. | ACTA MATHEMATICA SINICA-ENGLISH SERIES , 2015 , 31 (8) : 1261-1272 . |
| MLA | Zhang, Yun Nan 等. "Two classes of operators with irreducibility and the small and compact perturbations of them" . | ACTA MATHEMATICA SINICA-ENGLISH SERIES 31 . 8 (2015) : 1261-1272 . |
| APA | Zhang, Yun Nan , Lin, Li Qiong . Two classes of operators with irreducibility and the small and compact perturbations of them . | ACTA MATHEMATICA SINICA-ENGLISH SERIES , 2015 , 31 (8) , 1261-1272 . |
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首先定义弱空间理想(￡)类奇异算子的概念,举例说明这类算子在一般情况下真包含严格奇异算子类,但在一定条件下二者又是相等的.然后证明了对给定的非平凡空间理想(￡),这类算子构成一内射闭算子理想W(￡)S,同时给出有界线性算子属于这个算子理想的充要条件.最后得到新的一种由非平凡空间理想生成算子理想的方法.
Keyword ：
Banach空间 Banach空间 弱空间理想 弱空间理想 空间理想 空间理想 算子理想 算子理想 (￡)类奇异算子 (￡)类奇异算子
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| GB/T 7714 | 赵旭 , 林丽琼 . 关于弱空间理想(￡)类奇异算子的探讨 [J]. | 福州大学学报（自然科学版） , 2014 , 42 (2) : 183-187 . |
| MLA | 赵旭 等. "关于弱空间理想(￡)类奇异算子的探讨" . | 福州大学学报（自然科学版） 42 . 2 (2014) : 183-187 . |
| APA | 赵旭 , 林丽琼 . 关于弱空间理想(￡)类奇异算子的探讨 . | 福州大学学报（自然科学版） , 2014 , 42 (2) , 183-187 . |
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Let A is an element of B(X) and B is an element of B(Y), MC be an operator on Banach space X circle plus Y given by M-C = [GRAPHICS] . A generalized Drazin spectrum defined by sigma D-g(T) = {lambda is an element of C : T - lambda I is not generalized Drazin invertible} is considered in this paper. It is shown that sigma D-g(A)boolean OR sigma D-g(B) = sigma D-g(M-C)boolean OR WgD(A, B, C), where WgD(A, B, C) is a subset of sigma D-g(A) boolean AND sigma D-g(B) and a union of certain holes in sigma D-g(M-C). Furthermore, several sufficient conditions for sigma D-g(A)boolean OR sigma D-g(B) = sigma D-g(M-C) holds for every C is an element of B(Y, X) are given.
Keyword ：
filling-in-hole problem filling-in-hole problem generalized Drazin spectrum generalized Drazin spectrum operator matrices operator matrices
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| GB/T 7714 | Zhang Shi-fang , Zhong Huai-jie , Lin Li-qiong . Generalized Drazin spectrum of operator matrices [J]. | APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B , 2014 , 29 (2) : 162-170 . |
| MLA | Zhang Shi-fang 等. "Generalized Drazin spectrum of operator matrices" . | APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B 29 . 2 (2014) : 162-170 . |
| APA | Zhang Shi-fang , Zhong Huai-jie , Lin Li-qiong . Generalized Drazin spectrum of operator matrices . | APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B , 2014 , 29 (2) , 162-170 . |
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