Dirichlet空间上Toeplitz算子的紧性

本文给出了 Ｄｉｒｉｃｈｌｅｔ空间上 Ｔｏｅｌｐｉｔｚ算子为紧算子的充要条件,并证明具有 Ｃ１－符号的 Ｔｏｅｐｌｉｔｚ算子为紧算子当且仅当它为零算子,当且仅当符号的边值为零．     

Dirchlet空间上ToePlitz算子的紧性

本文给出了Dirichlet空间上Toelpitz算子为紧算子的充要条件.并证明具有C     

The finite rank perturbations of the product of Hankel and Toeplitz operators

In this paper we completely characterize when the product of a Hankel operator and a Toeplitz operator on the Hardy space is a finite rank perturbation of a Hankel operator, and when the commutator of a Hankel operator and a Toeplitz operators has finite rank.     

Finite sums of Toeplitz products on the Dirichlet space

On the Dirichlet space of the unit disk, we consider a class of operators which contain finite sums of products of two Toeplitz operators with harmonic symbols. We give characterizations of when an operator in that class is zero or compact. Also, we solve the zero product problem for products of finitely many Toeplitz operators with harmonic symbols.     

加权Bergman空间上的紧算子

本文讨论了加权Ｂｅｒｇｍａｎ空间上的Ｔｏｅｐｌｉｔｚ算子,证明了Ｔｏｐｌｉｔｚ算子的有限乘积的有限和是紧的当且仅当它的Ｂｅｒｅｚｉｎ变换在边界上趋向于零．     

单位球Dirichlet空间上以拟齐次函数为符号的Toeplitz算子

In this paper, we study some algebraic properties of Toeplitz operators with quasihomogeneous symbols on the Dirichlet space of the unit ball Bn. First, we describe commutators of a radial Toeplitz operator and characterize commuting Toeplitz operators with quasihomogeneous symbols. Then we show that finite raak product of such operators only happens in the trivial case. Finally, some necessary and sufficient conditions are given for the product of two quasihomogeneous Toeplitz operators to be a quasihomogeneous Toeplitz operator.     

Algebraic properties and the finite rank problem for Toeplitz operators on the Segal-Bargmann space

We study three different problems in the area of Toeplitz operators on the Segal-Bargmann space in Cn. Extending results obtained previously by the first author and Y.L. Lee, and by the second author, we first determine the commutant of a given Toeplitz operator with a radial symbol belonging to the class Sym_>0(Cn) of symbols having certain growth at infinity. We then provide explicit examples of zero-products of non-trivial Toeplitz operators. These examples show the essential difference between Toeplitz operators on the Segal-Bargmann space and on the Bergman space over the unit ball. Finally, we discuss the “finite rank problem”. We show that there are no non-trivial rank one Toeplitz operators Tf for f∈Sym_>0(Cn). In all these problems, the growth at infinity of the symbols plays a crucial role.     

The distribution function inequality for a finite sum of finite products of Toeplitz operators

A generalized area function associated with a finite sum of finite products of Toeplitz operators is introduced. A distribution function inequality is established for the generalized area function. By using the distribution function inequality, we characterize when a finite sum of finite products of Toeplitz operators on the Hardy space is a compact perturbation of a Toeplitz operator.     

Generalized inversion of finite rank Hankel and Toeplitz operators with rational matrix symbols

The goal of the paper is a generalized inversion of finite rank Hankel operators and Hankel or Toeplitz operators with block matrices having finitely many rows. To attain it a left coprime fractional factorization of a strictly proper rational matrix function and the Bezout equation are used. Generalized inverses of these operators and generating functions for the inverses are explicitly constructed in terms of the fractional factorization.     

多圆盘上的Toeplitz算子的紧的乘积

对于多圆盘上的有界多重调和函数f,g,我们证明多圆盘Bergman空间上的Toeplitz算子的乘积TfTg是紧算子的充要条件是TfTg是零.这等价于f或g是零.换位子TfTg-TgTf是紧算子当且仅当换位子TfTg-TgTf是零.这等价于对每一个j,存在不全为零的常数αj和βj,使得αjf+βjg关于变量zj(1≤j≤n)是常数.     

有界对称区域上Dirichlet空间中的紧Toeplitz算子

介绍了有界对称区域Ω上Dirichlet空间中的Toeplitz算子的紧性:如果S是有限个Toeplitz算子乘积的有限和,S是紧算子当且仅当S的Berezin变换S(z)趋于0.     

Algebraic properties of Toeplitz operators on the Dirichlet space

We study some algebraic properties of Toeplitz operators on the Dirichlet space. We first characterize (semi-)commuting Toeplitz operators with harmonic symbols. Next we study the product problem of when product of two Toeplitz operators is another Toeplitz operator. As an application, we show that the zero product of two Toeplitz operators with harmonic symbol has only a trivial solution. Also, the corresponding compact product problem is studied.     

Toeplitz Operators on the Dirichlet Space

In this paper a decomposition of Sobolev space is obtained. Then we prove that a Toeplitz operator on the Dirichlet space is compact only when it is the zero operator. For two Toeplitz operators on the Dirichlet space, we obtain the conditions for that they commute, their product is a Toeplitz operator, and their commutator or semi-commutator has finite rank, respectively.     

Properties of Toeplitz Operators on the Dirichlet Space Over the Ball

On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. Based on this, we characterize when finite sums of products of Toeplitz operators are of finite rank. Also, we give a necessary and sufficient condition for the commutator and semi-commutator of two Toeplitz operators being zero.     

Positivity of Toeplitz operators on harmonic Bergman space

In this paper, we study positive Toeplitz operators on the harmonic Bergman space via their Berezin transforms. We consider the Toeplitz operators with continuous harmonic symbols on the closed disk and show that the Toeplitz operator is positive if and only if its Berezin transform is nonnegative on the disk. On the other hand, we construct a function such that the Toeplitz operator with this function as the symbol is not positive but its Berezin transform is positive on the disk. We also consider the harmonic Bergman space on the upper half plane and prove that in this case the positive Toeplitz operators with continuous integrable harmonic symbols must be the zero operator.     

复合算子和一类解析Toeplitz算子的约化子空间

本文利用复合算子完全刻画了符号为两个Ｂｌａｓｃｈｋｅ因子乘积的解析Ｔｏｅｐｌｉｔｚ算子的约化子空间。     

调和Bergman空间上的Toeplitz的零积及有限秩性质

本文研究了调和Bergman空间上的Toeplitz的Brown-Halmos型零乘积问题以及有限秩的相关性质,并得到了以解析和余解析符号的Toeplitz算子乘积的有限和的零积有限秩的等价条件.     

斜Toeplitz算子的乘积和交换性

In this paper, the product and commutativity of slant Toeplitz operators are discussed. We show that the product of kth1-order slant Toeplitz operators and kth2-order slant Toeplitz operators must be a (k1k2) th-order slant Toeplitz operator except for zero operators, and the commutativity and essential commutativity of two slant Toeplitz operators with different orders are the same.     

单位多圆柱上Bergman空间中的分别准齐次ToePlitz算子

本文研究了单位多圆柱上Bergman空间中以分别准齐次函数为记号的Toeplitz算子的代数性质.我们首先得到了两个以分别准齐次函数为记号的Toeplitz算子可以写成一个Toeplitz算子的充分必要条件,然后利用L2(Dn,dV)的一个极分解式证明了,只要其中有一个Toeplitz算子是分别准齐次的,则其零乘积问题...     

多圆盘Bergman空间上Toeplitz算子的乘积和交换性

该文给出了多圆盘Bergman空间上两个带有某种符号的Toeplitz算子的乘积等于另一个Toeplitz算子的充分必要条件,并且给出了乘积算子所带符号的公式.接下来,相应的研究了它的交换性.这些研究结果都是根据符号函数的Mellin变换.