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Strong Laws of Large Numbers for Double Sums of Banach Space Valued Random Elements
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作者 Robert PARKER Andrew ROSALSKY 《数学学报:英文版》 SCIE CSCD 2019年第5期583-596,共14页
For a double array {Vm,n, m≥1,n≥1} of independent, mean 0 random elements in a real separable Rademacher type p (1≤p≤ 2) Banach space and an increasing double array {bm,n, m≥1,n ≥ 1} of positive constants, the l... For a double array {Vm,n, m≥1,n≥1} of independent, mean 0 random elements in a real separable Rademacher type p (1≤p≤ 2) Banach space and an increasing double array {bm,n, m≥1,n ≥ 1} of positive constants, the limit law max1≤k≤m,1≤l≤n||Σi/^k=1Σj/^l=1Vi,j||/bm,n → 0 a.c. and in Lp as m ∨n →∞ is shown to hold if Σm/^∞=1Σn/^∞=1E||Vm,n||^p/bm,n/^p<∞. This strong law of large numbers provides a complete characterization of Rademacher type p Banach spaces. Results of this form are also established when 0<p≤1 where no independence or mean 0 conditions are placed on the random elements and without any geometric conditions placed on the underlying Banach space. 展开更多
关键词 Real separable BANACH SPACE DOUBLE array of independent random elements strong law of large numbers almost sure CONVERGENCE Rademacher type p BANACH SPACE CONVERGENCE in Lp
Ring Isomorphisms and Complete Preservers of Fixed Points for Multipliers
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作者 Ting ZHANG Jinchuan HOU 《数学研究及应用:英文版》 CSCD 2019年第1期89-100,共12页
Let R1 and R2 be two rings with unit I.We give some characterizations of ring homomorphisms and ring isomorphisms between R1 and R2 in term of complete preservers of fixed points of multipliers,under some mild assumpt... Let R1 and R2 be two rings with unit I.We give some characterizations of ring homomorphisms and ring isomorphisms between R1 and R2 in term of complete preservers of fixed points of multipliers,under some mild assumption on R1.Applications to several kinds of operator algebras such as Banach algebras,nest algebras,matrix algebras and standard operator algebras are presented. 展开更多
关键词 COMPLETE preserver problem BANACH algebra RING ISOMORPHISM operator on BANACH space
Additive Maps Preserving Nilpotent Perturbation of Scalars
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作者 Ting ZHANG Jin Chuan HOU 《数学学报:英文版》 SCIE CSCD 2019年第3期407-426,共20页
Let X be a Banach space over F(= R or C) with dimension greater than 2. Let N(X) be the set of all nilpotent operators and B0(X) the set spanned by N(X). We give a structure result to the additive maps on FI + B0(X) t... Let X be a Banach space over F(= R or C) with dimension greater than 2. Let N(X) be the set of all nilpotent operators and B0(X) the set spanned by N(X). We give a structure result to the additive maps on FI + B0(X) that preserve rank-1 perturbation of scalars in both directions. Based on it, a characterization of surjective additive maps on FI + B0(X) that preserve nilpotent perturbation of scalars in both directions are obtained. Such a map Φ has the form either Φ(T) = cAT A-1+ φ(T)I for all T ∈ FI + B0(X) or Φ(T) = cAT*A-1+ φ(T)I for all T ∈ FI + B0(X), where c is a nonzero scalar,A is a τ-linear bijective transformation for some automorphism τ of F and φ is an additive functional.In addition, if dim X = ∞, then A is in fact a linear or conjugate linear invertible bounded operator. 展开更多
关键词 BANACH spaces NILPOTENT operators PERTURBATIONS additive PRESERVERS
STABILITY OF A PAIR OF BANACH SPACES FOR ε-ISOMETRIES 预览
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作者 戴端旭 郑本拓 《数学物理学报:B辑英文版》 SCIE CSCD 2019年第4期1163-1172,共10页
A pair of Banach spaces (X, Y) is said to be stable if for every £-isometry f : X→Y,there exist γ> 0 and a bounded linear operator T : L(f)→X with ||T||≤α such that ||Tf(x)- x||≤γε for all x ∈ X, where L(... A pair of Banach spaces (X, Y) is said to be stable if for every £-isometry f : X→Y,there exist γ> 0 and a bounded linear operator T : L(f)→X with ||T||≤α such that ||Tf(x)- x||≤γε for all x ∈ X, where L(f) is the closed linear span of f(X). In this article, we study the stability of a pair of Banach spaces (X, Y) when X is a C(K) space. This gives a new positive answer to Qian's problem. Finally, we also obtain a nonlinear version for Qian's problem. 展开更多
关键词 STABILITY ε-isometry Figiel THEOREM BANACH space
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Bloch-type spaces and extended Cesàro operators in the unit ball of a complex Banach space
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作者 Hidetaka Hamada 《中国科学:数学英文版》 SCIE CSCD 2019年第4期617-628,共12页
Let B be the unit ball of a complex Banach space X. In this paper, we generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball B by using the radial derivative. Next, we define an extend... Let B be the unit ball of a complex Banach space X. In this paper, we generalize the Bloch-type spaces and the little Bloch-type spaces to the open unit ball B by using the radial derivative. Next, we define an extended Cesaro operator Tφ with the holomorphic symbol φ and characterize those φ for which Tφ is bounded between the Bloch-type spaces and the little Bloch-type spaces. We also characterize those φ for which Tφ is compact between the Bloch-type spaces and the little Bloch-type spaces under some additional assumption on the symbol φ. When B is the open unit ball of a finite dimensional complex Banach space X, this additional assumption is automatically satisfied. 展开更多
关键词 Bloch-type SPACE COMPLEX Banach SPACE EXTENDED CESARO operator little Bloch-type SPACE
Every Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff measure
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作者 Ehmet Abler Lixin Cheng +1 位作者 Qingjin Cheng Wen Zhang 《中国科学:数学英文版》 SCIE CSCD 2019年第1期147-156,共10页
In this paper, we show that every infinite dimensional Banach space admits a homogenous measure of non-compactness not equivalent to the Hausdorff measure. Therefore, it resolves a long-standing question.
关键词 measure of non-compactness inequivalence BANACH space
具有Banach代数的半序锥b-度量空间的一类改进(英文) 预览
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作者 韩艳 许绍元 董延寿 《数学季刊:英文版》 2019年第1期43-51,共9页
The purpose of this paper is to improve some famous theorems for contractive mapping from ρ(α + β) ∈ [0,1/s) to ρ(α + β) ∈ [0, 1) in ordered cone b-metric spaces over Banach algebras with coefficient s ≥ 1(ρ... The purpose of this paper is to improve some famous theorems for contractive mapping from ρ(α + β) ∈ [0,1/s) to ρ(α + β) ∈ [0, 1) in ordered cone b-metric spaces over Banach algebras with coefficient s ≥ 1(ρ(x) is the spectral radius of the generalized Lipschitz constant x). Moreover, some similar improvements in ordered cone b-metric spaces are also obtained, which from α + β∈ [0,1/s) to α + β∈ [0, 1). Some examples are given to support that our new results are genuine improvements and generalizations. 展开更多
关键词 Cone b-metric spaces over BANACH ALGEBRAS c-distance generalized LIPSCHITZ MAPPINGS fixed point
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HYPERCYCLIC MULTIPLICATION COMPOSITION OPERATORS ON WEIGHTED BANACH SPACE
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作者 Cui Wang Huiqiang Lu 《应用数学年刊:英文版》 2019年第2期189-196,共8页
This paper characterizes some sufficient and necessary conditions for the hypercyclicity of multiples of composition operators on Hlog,0∞.
关键词 composition OPERATORS HYPERCYCLIC WEIGHTED BANACH space
Stability Characterizations of ε-isometries on Certain Banach Spaces
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作者 Li Xin CHENG Long Fa SUN 《数学学报:英文版》 SCIE CSCD 2019年第1期123-134,共12页
Suppose that X, Y are two real Banach Spaces. We know that for a standard ε-isometry f : X → Y, the weak stability formula holds and by applying the formula we can induce a closed subspace N of *. In this paper, by ... Suppose that X, Y are two real Banach Spaces. We know that for a standard ε-isometry f : X → Y, the weak stability formula holds and by applying the formula we can induce a closed subspace N of *. In this paper, by using again the weak stability formula, we further show a sufficient and necessary condition for a standard ε-isometry to be stable in assuming that N is w*-closed in Y*.Making use of this result, we improve several known results including Figiel’s theorem in reflexive spaces.We also prove that if, in addition, the space Y is quasi-reflexive and hereditarily indecomposable, then L(f)≡span[f(X)] contains a complemented linear isometric copy of X;Moreover, if X =Y, then for every e-isometry f: X → X, there exists a surjective linear isometry S:X → X such that f-S is uniformly bounded by 2ε on X. 展开更多
关键词 ε-isometry STABILITY hereditarily INDECOMPOSABLE SPACE quasi-reflexive SPACE Banach SPACE
A NOTE IN APPROXIMATIVE COMPACTNESS AND MIDPOINT LOCALLY K-UNIFORM ROTUNDITY IN BANACH SPACES 预览
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作者 刘春燕 张子厚 周宇 《数学物理学报:B辑英文版》 SCIE CSCD 2018年第2期643-650,共8页
在这篇文章,我们证明下列结果:(1 ) Banach 空间 X 局部地是弱中点 k 一致地圆胖如果并且仅当 X 的每个关上的球是一近似地,弱紧缩的 k-Chebyshev 设定;(2 ) Banach 空间 X 局部地是中点 k 一致地圆胖如果并且仅当 X 的每个关上的... 在这篇文章,我们证明下列结果:(1 ) Banach 空间 X 局部地是弱中点 k 一致地圆胖如果并且仅当 X 的每个关上的球是一近似地,弱紧缩的 k-Chebyshev 设定;(2 ) Banach 空间 X 局部地是中点 k 一致地圆胖如果并且仅当 X 的每个关上的球是一个近似地紧缩的 k-Chebyshev 集合。 展开更多
关键词 BANACH 中点 BANACH 笔记 空格 制服 空间 弱紧
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一类常微分方程初值问题解的存在与唯一 预览
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作者 施敏 《沈阳大学学报:自然科学版》 CAS 2018年第4期342-344,共3页
利用Banach压缩映射原理,研究了一类三阶常微分方程初值问题解的存在性和唯一性,并利用MATLAB软件对相关微分方程初值问题进行了数值仿真.
关键词 BANACH 初值问题 MATLAB 数值仿真
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Recurrence of Transitive Points in Dynamical Systems with the Specification Property
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作者 Xiao Yi WANG Yu HUANG 《数学学报:英文版》 SCIE CSCD 2018年第12期1879-1891,共13页
关键词 系统 性质 BANACH 复发 周期性 集合 BR 构造点
On the Coefficient Inequality for A Subclass of Starlike Mappings in Several Complex Variables 预览
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作者 GUO Sheng-ti XU Qing-hua 《数学季刊:英文版》 2018年第1期98-110,共13页
关键词 星形 子类 BANACH 函数
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Operator algebras associated with multiplicative convolutions of arithmetic functions
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作者 Aiju Dong Linzhe Huang Boqing Xue 《中国科学:数学英文版》 SCIE CSCD 2018年第9期1665-1676,共12页
关键词 代数学 操作员 算术 NEUMANN 旋转 卷绕 BANACH 素数
On p-convergent Operators on Banach Lattices
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作者 Elroy D. ZEEKOEI Jan H. FOURIE 《数学学报:英文版》 SCIE CSCD 2018年第5期873-890,共18页
关键词 BANACH 操作员 会聚 格子 应用程序 向量函数 性质 操作符
Fekete and Szego problem in one and higher dimensions
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作者 Qinghua Xu Taishun Liu Xiaosong Liu 《中国科学:数学英文版》 SCIE CSCD 2018年第10期1775-1788,共14页
关键词 尺寸 BANACH 函数 CN
PRODUCTS OF WEIGHTED COMPOSITION AND DIFFERENTIATION OPERATORS INTO WEIGHTED ZYGMUND AND BLOCH SPACES 预览
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作者 Jasbir Singh MANHAS Ruhan ZHAO 《数学物理学报:B辑英文版》 SCIE CSCD 2018年第4期1105-1120,共16页
关键词 加权 空格 产品 操作员 BANACH 操作符 函数
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On Quasi-Chebyshevity Subsets of Unital Banach Algebras 预览
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作者 M. Iranmanesh F. Soleimany 《分析理论与应用:英文刊》 CSCD 2018年第1期92-102,共11页
关键词 BANACH 代数学 子集 CHEBYSHEV HILBERT 无限维 集合
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Existence and uniqueness results for mild solutions of random impulsive abstract neutral partial differential equation over real axis 预览
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作者 P Indhumathi A Leelamani 《高校应用数学学报:英文版(B辑)》 SCIE CSCD 2018年第1期71-87,共17页
In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-S... In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-Schauder Alternative and Banach Contraction Principle.Finally an example is given to illustrate our problem. 展开更多
关键词 neutral equation LERAY SCHAUDER Alternative BANACH CONTRACTION Principle SEMIGROUP of linear operators
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The Estimates of All Homogeneous Expansions for a Subclass of e Quasi-convex Mappings in Several Complex Variables
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作者 Xiaosong LIU Taishun LIU 《数学年刊:B辑英文版》 SCIE CSCD 2018年第4期621-632,共12页
关键词 伪凸 估计 同类 子类 BANACH
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