A^p（φ）上Toeplitz算子的换位子

本文使用不变加权面积平均值性质刻画了单位圆盘内的调和函数．由此我们探讨了加权Bergman空间A^p(φ)上的Toeplitz算子，给出了两个具有界调和符号的Toeplitz算子交换或本质交换的一些充要条件．     

Ap(ψ)上Toeplitz算子的换位子

本文使用不变加权面积平均值性质刻画了单位圆盘内的调和函数.由此我们探讨了加权Bergman空间Ap(ψ)上的Toeplitz算子,给出了两个具有界调和符号的Toeplitz算子交换或本质交换的一些充要条件.     

Ap(ψ)上Toeplitz算子的半换位子

本文给出加权Bergman空间Ap(ψ)上具有界调和符号的Toeplitz算子的半换位子为零或为紧算子的一些充要条件.     

Ap(φ)上Toeplitz算子的半换位子

本文给出加权Bergman空间A^p(φ)上具有界调和符号的Toeplitz算子的半换位子为零或为紧算子的一些充要条件.     

Hardy空间上一类$m$-复对称Toeplitz算子

本文主要研究Toeplitz算子相对于一对置换的共轭算子是2-复对称的充要条件. 首先在经典的Hardy空间上介绍一类被称为一对置换的共轭算子, 其次完整地刻画了在这类共轭算子下Toeplitz算子是2-复对称的结构, 利用Toeplitz算子在Hardy空间的经典正规正交基下的矩阵表示来刻画2-复对称Toeplitz算子. 最后对于Toeplitz算子分别补充前提$f_n=-f_{-n}$和$f_n=f_{-n}$, 得到了更简化的结果. 在第二个前提下, 研究Toeplitz算子的3-复对称性, 得到$T_f$关于$C_{(i,j)}$是3-CSO的结果和是2-CSO相同.     

多重圆盘上的Toeplitz代数

本文研究了H~2(T~n)上由符号为本性有界可测函数的Toeplitz算子生成的C~*-代数的结构,并得到了这样的Toeplitz算子的一些谱性质.     

有限秩Toeplitz算子的(半)换位子

获得了Bergman空间上形如(T_f,T_g]-T_(h~n)和[T_f,T_g]-T_(h~n)的算子为有限秩时的充要条件,其中f,g,h均为有界调和函数,n为非负自然数.     

Commutators and Semi-commutators of Monomial Toeplitz Operators on the Pluriharmonic Hardy Space

In this paper, the authors completely characterize the finite rank commutator and semi-commutator of two monomial Toeplitz operators on the pluriharmonic Hardy space of the torus or the unit sphere. As a consequence, many non-trivial examples of(semi-)commuting Toeplitz operators on the pluriharmonic Hardy spaces are given.     

Commuting Toeplitz operators on the Hardy space of the bidisk

On the Hardy space of the bidisk, we give a necessary and sufficient condition for a bounded symbol of a Toeplitz operator that commutes with another Toeplitz operator whose symbol is a certain type of bounded symbol.     

Commuting Toeplitz Operators on the Pluriharmonic Bergman Space

We prove that two Toeplitz operators acting on the pluriharmonic Bergman space with radial symbol and pluriharmonic symbol respectively commute only in an obvious case.     

Toeplitz products with pluriharmonic symbols on the Hardy space over the ball

On the Hardy space over the unit ball in Cn, we consider operators which have the form of a finite sum of products of several Toeplitz operators. We study characterizing problems of when such an operator is compact or of finite rank. Some of our results show higher-dimensional phenomena.     

Mixed Product of Hankel and Toeplitz Operators on Fock-Sobolev Spaces

Let f and g be functions in Fock-Sobolev space F^2,m. In this paper, we completely characterize the boundedness and compactness of H_f T_g.     

Bergman空间上一类解析Toeplitz算子的强不可约性

令D为单位圆盘D={z∈C:|z|<1},L_a~2(D)为L~2(D)中解析函数构成的Bergman空间.设f(z)=a_0+a_1z+a_2z~2+…,用算子理论的技巧给出解析Toeplitz算子T_f为强不可约算子的一个充分条件.     

重调和Hardy空间Toeplitz算子的交换性

本文研究重调和Hardy空间h~2(Ω)上,Toeplitz算子的交换性,给出了h~2(T~2)上一个解析Toeplitz算子与另一个共轭解析Toeplitz算子交换的充分必要条件.     

Algebraic Properties of Generalized Toeplitz Operators

§ 1.Introduction　 Let D be the unit disk of the complex plane C,T the unit circle,and H2 the Hardyspace of the unit circle.For operators on H2 ,all matrices in the sequel will be formedwith respect to the basis { e0 ,e1 ,… } defined by en(z) =zn,n=0 ,1 ,2 ,… . Ifφ∈ L∞ (T) ,write Tφfor the corresponding Toeplitz operator defined on H2 by Tφf=P(φf) (where Pis the projection from L2 (T) onto H2 ) .The Toeplitz operator Te1,the so called unilat-eral shift,will be denoted by U thr…     

Commuting Dual Toeplitz Operators on the Polydisk

On the polydisk, the commutativity of dual Toeplitz operators is studied. We obtain characterizations of commuting dual Toeplitz operators, essentially commuting dual Toeplitz operators and essentially semi-commuting dual Toeplitz operators.