可列谱的仿正规算子是正规算子

本文中,总设H是复平面C上的Hilbert空间,φ(H)是H上的线性有界算子全体。设T∈(H),称T为仿正规算子。若对所有x∈H,‖Tx‖~2 ‖T~2x‖ ‖x‖。易知半亚正规算子(因而亚正规算子)是仿正规算子。仿正规算子的正规性条件是一个引人注意的问题。1972年,T.Saito在其专著[1]中提出了一个问题:多项式紧的仿正规算子是否正规算子?1982年,文[2]指出多项式紧的仿正规算子必是正规算子的紧摄动。本文中,我们利用超穷     

Bergman空间L_a~1(Ω)上的Toeplitz和Hankel算子

本文讨论了 Bergman空间 L1a(Ω )中 Toeplitz和 Hankel算子的 W* 紧性 ,得到与 L2a(Ω )上 T- H算子紧性 [4]类似的某些结果     

Bergman空间L^1a（Ω）上的Toeplitz和Hankel算子

本文讨论了Bergman空间L^1a(Ω)中Toeplitz和Hankel算子的W^*紧性,得到与L^2a(Ω)上T－H算子紧性^[4]类似的某些结果。     

Hilbert空间上线性算子广义逆A_(T,S)~((2))的存在性及其表示式

设H1和H2是两个Hilbert空间,B(H1,H2)表示从H1到H2的所有有界线性算子的集合,T和S分别是H1和H2的两个闭子空间．如果存在线性算子X∈B(H2,H1)满足XAX=X,R(X)=T,N(X)=S,则称X为线性算子A的具有指定像空间T和零空间S的外逆,记为AT,S(2)．该文进一步研究了线性算子广义逆AT,S(2)存在的若干等价条件及其性质,建立了算子广义逆AT,S(2)的表示形式．     

上三角算子矩阵的单值延拓性质的摄动

设H为无限维可分的复Hilbert空间,B(H)为H上的有界线性算子全体.算子T∈B(H)称为具有单值延拓性质,若对任意一个开集U(?)C,满足方程(T-λI)f(λ)=0(任给λ∈U)的唯一的解析函数f:U→H为零函数;T∈B(H)称为满足单值延拓性质的稳定性,若对任意一个紧算子K∈B(H),T+K都满足单值延拓性质.本文给出了2×2上三角算子矩阵在紧摄动下满足单值延拓性质的稳定性的特征.     

一类次线性算子在局部紧Vilenkin群上Herz型Hardy空间上的有界性

设 G是局部紧的 Vilenkin群 .本文研究了一类具有分数次积分性质的次线性算子从 H Kα,p1q1(G)到 (弱 ) H Kα,p2q2 (G)有界的判别条件 .     

模糊蕴涵与Smooth紧

1985年,Sostak[8]由逻辑的观点出发定义了一种基于Lukasiew icz蕴涵算子的Sm ooth紧,基于同样的思想A.H aydar E s[12]又定义了另外几种Sm ooth(fuzzy)紧并讨论了它们之间的关系。王国俊教授[10]提出了一种比Lukasiew icz算子具有更好性质的R0-算子,基于R0-算子我们定义了一种模糊蕴涵,通过这种模糊蕴涵定义几种Sm ooth紧并讨论了它们的一些性质。     

圆环上Dirichlet空间中的Toeplitz算子及其代数性质

主要讨论了:(1)圆环上Dirichlet空间D~p(1P+∞),以φ∈L~(∞,1)为符号的Toeplitz算子T_φ的紧性等价条件-T_φ的Berezin变换在圆环的两边界上为0;(2)圆环上Dirichlet空间D~2,以u∈C~1(M)为符号的Toeplitz算子T_u的性质,并得到典型分解式:S=T_S+R,其中R为换位子,S=T_(uij).     

广义Kato分解与Weyl型定理的摄动

称T∈B(H)有广义Kato分解,若存在一对T的闭的不变子空间(M,N)使得H=M⊕Ⅳ,其中T|_M为上半Fredholm算子且具有非负的指标,T|_N是幂零的本文利用算子的广义Kato分解性质,研究了Weyl型定理在紧摄动下的稳定性.此外还研究了2×2上三角算子矩阵的Weyl型定理在紧摄动下的稳定性.     

包含广义逆的算子乘积的谱

给定三个算子A,B,C∈ B(H),其中算子B的值域R(B)是闭的,利用算子矩阵分块技巧给出了∪σ(AB(1))C)=C的充分必要条件,其中σ(D)是算子D ∈B(H)的B(1) ∈B{1}谱,B{1}={X∈B(H):B×B=B}.     

Banach 空间上算子的几种不可约性

本文根据Cowen-Douglas 算子的定义引入两类与强不可约算子有紧密联系的算子类— B_n 算子与B 算子. 说明了在可分Banach 空间上存在B_n 算子与B 算子. 文章详细讨论了几种具有不可约性的算子类之间的关系并得到了一个关系图. 本文还给出这些算子类的一些性质, 包括算子的(拟) 相似不变性等.     

Rate of approximation for functions with derivatives of bounded variation

We estimate pointwise convergence rates of approximation for functions with derivatives of bounded variation and for functions which are exponentially bounded and have derivatives locally of bounded variation. The approximation is made through the operation of a sequence of integral operators with not necessarily positive kernel functions. The general result is then applied to deduce estimates for Beta operators, Hermite-Fejér operators, Picard operators, Gauss-Weierstrass operators, Baskakov operators, Mirakjan-Szász operators, Bleimann-Butzer-Hahn operators, Phillips operators, and Post-Widder operators.     

Disturbing Fuzzy Propositional Logic and its Operators

In this paper, the concept of disturbing fuzzy propositional logic is introduced, and the operators of disturbing fuzzy propositions is defined. Then the 1-dimensional truth value of fuzzy logic operators is extended to be two-dimensional operators, which include disturbing fuzzy negation operators, implication operators, “and” and “or” operators and continuous operators. The properties of these logic operators are studied.     

Dirichlet空间上Toeplitz算子与Berezin型变换相关的一些性质

本文研究了单位圆盘D 的Dirichlet 空间上Toeplitz 算子和小Hankel 算子. 利用Berezin 型变换讨论了Toeplitz 算子的不变子空间问题, 具有Berezin 型符号的Toeplitz 算子的渐进可乘性以及Toeplitz 算子的Riccati 方程的可解性. 应用Berezin 变换得到了Toeplitz 算子和小Hankel 算子可逆的充分条件. 此外, 还利用Hankel 算子和Berezin 变换刻画了算子2T_uv-T_uT_v-T_vT_u 的紧性, 其中函数u,v ∈ L^2,1.     

Fixed points of generalized e-concave (generalized e-convex) operators and their applications

In this paper, we present the definitions of generalized e-concave operators and generalized e-convex operators, which are the generalizations of e-concave operators and e-convex operators, respectively. Without compactness or continuity assumption of generalized e-concave operators and generalized e-convex operators, we have proved the existence, uniqueness and monotone iterative techniques of their fixed points. Our results are even new to e-concave operators and e-convex operators. Finally, we apply the results to the singular boundary value problems for second order differential equations.     

一类新型非正规算子的谱分析

本文引入了一类新型非正规算子,即具复谱的u-标算子.证明了该类算子具有Jordan型分解,讨论了u-标算子与标型谱算子的关系,并通过例子说明了该类算子的构造.     

Banach格上的b-几乎Dunford-Pettis算子

首先给出了Banah格上的b-几乎Dunford-Pettis算子的定义;其次,研究了b-几乎Dunford-Pettis算子的相关性质,如b-几乎Dunford-Pettis算子的等价刻画,构成空间的性质,以及控制性;最后,研究了b-几乎DunfordPettis算子与相关算子(b-弱紧算子,弱紧算子,几乎Dunford-Pettis算子)间的关系.     

Boundedness of sublinear operators in weighted grand Morrey spaces

The boundedness of sublinear integral operators in grand Morrey spaces defined by means of measures generated by the Muckenhoupt weights is established. The operators under consideration involve operators of Harmonic Analysis such as Hardy–Littlewood and fractional maximal operators, Calderoń–Zygmund operators, potential operators etc.     

Equivalence after extension and Schur coupling coincide for inessential operators

In recent years the coincidence of the operator relations equivalence after extension (EAE) and Schur coupling (SC) was settled for the Hilbert space case. For Banach space operators, it is known that SC implies EAE, but the converse implication is only known for special classes of operators, such as Fredholm operators with index zero and operators that can in norm be approximated by invertible operators. In this paper we prove that the implication EAE $?$ SC also holds for inessential Banach space operators. The inessential operators were introduced as a generalization of the compact operators, and include, besides the compact operators, also the strictly singular and strictly co-singular operators; in fact they form the largest ideal such that the invertible elements in the associated quotient algebra coincide with (the equivalence classes of) the Fredholm operators.     

Norm Inequalities for Fractional Integral Operators on Generalized Weighted Morrey Spaces

Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds,the fractional integral operators with rough kernels and fractional maximal operators with rough kernels as special cases,we prove that if these operators are bounded on weighted Lebesgue spaces and satisfy some local pointwise control,then these operators and the commutators of these operators with a BMO functions are also bounded on generalized weighted Morrey spaces.