Hibert空间中广义框架的非交性

引入了Hilbert空间H中广义框架的非交性、强非交性,讨论了它们的一些性质;并且引入了保非交算子、强保非交算子,证明了酉算子、可逆算子是强保非交算子,下有界算子、余等距算子是保非交算子.     

Feller-Trotter概率型算子对有界变差函数的收敛速度

本文运用概率方法研究了Feller-Trotter概率型算子对有界变差函数的收敛速度。由于该算子包括许多常见的算子,从而由关于该算子的一般结论可导出许多常见算子对有界变差。函数的收敛速度。作为一般结论的应用,本文列举了Baskakov算子、Szasz-Mirakjan算子、Gauss-Weierstrass算子、Gramma算子、Post-Gamma算子对有界变差函数的收敛速度。其中,关于Szasz-Mirakjan算子的结论推广并改进了Fuhua Cheng的结论,其它结论是作者首次得到。     

四参数区间数调和平均算子及其决策应用北大核心

将三参数区间数有序加权调和平均算子(CP-OWHA)推广到四参数区间数,提出了四参数区间数有序加权调和平均算子(CFP-OWHA),在此基础上定义了四参数区间数组的加权调和CFP-OWHA算子、有序加权调和CFP-OWHA算子、组合CFP-OWHA算子以及广义加权调和CFP-OWHA算子、广义有序加权调和CFP-OWHA算子和广义组合CP-OWHA算子,并探讨了它们的一些性质。然后,提出了基于四参数区间数调和平均算子的决策方法.最后,通过实例说明了决策方法的可行性。     

直觉不确定语言Frank集结算子及其应用

基于直觉不确定语言变量和Frank算子,提出了直觉不确定语言Frank集结算子的概念,给出了直觉不确定语言Frank集结算子的运算规则、期望函数、大小比较方法;定义了直觉不确定语言Frank加权算术平均算子、加权几何平均算子、有序加权算术平均算子、有序加权几何平均算子、广义加权平均算子以及算子具有的幂等性、单调性、有界性等性质.并基于这些算子提出两种属性权重确知且属性值以直觉不确定语言形式给出的决策方法,最后通过实例验证了方法的可行性.     

离散交换群上Toeplitz 算子的代数性质

广泛的意义下定义 Toeplitz 算子, 给出了Toeplitz 算子乘积仍为Toeplitz 算子的充分必要条件, Toeplitz算子是正规算子的充分必要条件以及 Toeplitz 算子可交换的一个必要条件,从而推广了经典 Toeplitz 算子的相应结果.     

Banach格上的b-Dunford-Pettis算子

为了进一步研究Banach格上算子的性质,受b-序有界集和Dunford-Pettis集定义的启发,给出了b-Dunford-Pettis算子的定义,研究了该算子与b-AM-紧算子(Dunford-Pettis全连续算子,弱极限算子,序Dunford-Pettis算子)间的关系;利用b-Dunford-Pettis算子与Dunford-Pettis算子的共轭关系,证明了b-Dunford-Pettis算子满足控制性.     

线性缓冲算子矩阵及其应用研究

在缓冲算子公理体系下,构造了一类线性的弱化缓冲算子和强化缓冲算子,并定义了这类缓冲算子的算子矩阵,研究了它们的一些特性,并以此证明了m阶算子作用的计算公式,最后实例验证了算子的有效性与实用性.     

冯·诺依曼代数的可测算子的性质

本文研究了冯·诺依曼代数的可测算子的基本性质,定义了阶梯算子,证明了任意一个正可测算子可以由阶梯算子在定义域内按照强算子拓扑逼近,从而证明了任意一个可测算子可以由投影在定义域内按照强算子拓扑逼近.此外,还讨论了可测算子与有界算子的复合算子的可测性.     

含参量蕴涵算子的构造及其性质

从空间几何的角度给出了几类含参量蕴涵算子，它们可以将常见的三种蕴涵算子Lukasiewicz算子、如算子及Godel算子包含其中，此外，还讨论了蕴涵算子的正则性质。     

投影对的广义投影束的性质

设T∈B(H)是Hilbert空间H上的有界线性算子,本文研究了算子投影对(P,Q)和复数对(α,β)的广义投影束T=P+αQ+βPQ的性质.用投影算子的Halmos分解定理,得到了算子T为广义投影束的一些等价条件,给出了广义投影束T的谱性质,证明了广义投影束T在一定条件下与对角算子相似的性质,建立起广义投影束T的谱跟投影P和Q的谱之间的关系.最后,讨论了广义投影束T为特殊算子类,例如Fredholm算子、紧算子、自伴算子的充要条件,并给出了算子T关于幂等对的广义投影束的几个性质.     

On infinite dimensional quadratic Volterra operators

In this paper we study a class of quadratic operators named by Volterra operators on infinite dimensional space. We prove that such operators have infinitely many fixed points and the set of Volterra operators forms a convex compact set. In addition, it is described its extreme points. Besides, we study certain limit behaviors of such operators and give some more examples of Volterra operators for which their trajectories do not converge. Finally, we define a compatible sequence of finite dimensional Volterra operators and prove that any power of this sequence converges in weak topology.     

Localized Frames and Compactness

We introduce the concept of weak localization for continuous frames and use this concept to define a class of weakly localized operators. This class contains many important classes of operators, including: short time Fourier transform multipliers, Calderon–Toeplitz operators, Toeplitz operators on various functions spaces, Anti-Wick operators, some pseudodifferential operators, some Calderon–Zygmund operators, and many others. In this paper, we study the boundedness and compactness of weakly localized operators. In particular, we provide a characterization of compactness for weakly localized operators in terms of the behavior of their Berezin transforms.     

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.     

On h-unitary and block-toeplitz h-normal operators

A special class of normal operators acting in spaces with indefinite scalar products is studied. The operators from this class are characterized by the property that, in a natural basis, their matrices have diagonal block-Toeplitz forms. The relations between polynomials of self-adjoint operators and operators from this class are established.     

On h-unitary and block-toeplitz h-normal operators

A special class of normal operators acting in spaces with indefinite scalar products is studied. The operators from this class are characterized by the property that, in a natural basis, their matrices have diagonal block-Toeplitz forms. The relations between polynomials of self-adjoint operators and operators from this class are established.     

Asymptotic Toeplitz and Hankel operators on the Bergman space

In this paper the concept of asymptotic Toeplitz and asymptotic Hankel operators on the Bergman space are introduced and properties of these classes of operators are studied. The importance of this notion is that it associates with a class of operators a Toeplitz operator and with a class of operators a Hankel operator where the original operators are not even Toeplitz or Hankel. Thus it is possible to assign a symbol to an operator that is not Toeplitz or Hankel and hence a symbol calculus is obtained. Further a relation between Toeplitz operators and little Hankel operators on the Bergman space is established in some asymptotic sense.     

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.     

Local smoothing for operators failing the cinematic curvature condition

In this paper, we examine a class of averaging operators which exhibit local smoothing. That is, viewed as a function of space and time variables, the operators yield more smoothing than the fixed-time estimates. Sogge showed in a more general setting that if these operators satisfy a cinematic curvature condition, they will exhibit some local smoothing [C.D. Sogge, Propagation of singularities and maximal functions in the plane, Invent. Math. 104 (1991) 231-251]. Here we translate this condition into the setting of averaging operators in the plane. We prove that cinematic curvature is not necessary for local smoothing to occur, exhibiting a class of operators which fail the cinematic curvature condition but still satisfy a local smoothing estimate. Furthermore, the amount of local smoothing exhibited by these operators is strictly less than that conjectured for operators satisfying the cinematic curvature condition.     

On positive almost weak* Dunford–Pettis operators

In this paper, we introduce the class of almost weak* Dunford–Pettis operators and give a characterization of this class of operators. We study its relation with the classes of weak* Dunford–Pettis operators and almost Dunford–Pettis operators, and its relation with the closely related classes of almost limited operators and L-weakly compact operators.     

On a Class of Non-local Operators in Conformal Geometry

In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study of a class of fourth order operators and their third order boundary operators. These third order operators are generalizations of the Dirichlet-to-Neumann operator.