调和Dirichlet空间D_h~1上有界、紧与Fredholm的Toeplitz算子

该文讨论了调和Dirichlet空间D_h~1上Toeplitz与Hankel算子的有界性、紧性与Fredholm性质,计算了Toeplitz算子的Fredholm指标.     

调和Dirichlet空间上的Toeplitz算子

刻画了调和Dirichlet空间上Toeplitz算子的有界性、紧性,讨论了Toeplitz算子的代数性质,得到了Toeplitz代数与Hankel代数的短正合列.还计算了Toeplitz代数与Hankel代数中Fredholm算子的Fredholm指标,得到了Toeplitz代数与Hankel代数的K_0与K_1群.     

Hardy空间H~1(S)上Toeplitz算子的Fredholm性质

本文讨论了Toeplitz算子在Hardy空间H1(S)上的Fredholm性质.证明了在单位球面S上处处不为零的连续函数φ具有对数有界平均振动时,以其为符号的Toeplitz算子Tφ是Fredholm算子,并且此时Tφ的指标为零.     

Dirichlet空间上Toeplitz算子的一些性质

该文研究了Dirichlet空间D^p~(1< p<∞)上Toeplitz算子的紧性与Fredholm性质, 计算了D^p上Toeplitz算子的Fredholm指标. 还考查了D^p上Hankel算子紧性.     

加权Bergman空间上Toeplitz算子的本质谱

本文探讨加权Bergman空间Ap(φ)上Toeplitz算子,刻画了L∞(D)的使得符号在其中的Toeplitz算子的半换位子是紧算子的最大的自伴子代数Q,并计算了符号在Q中的Toeplitz算子的本质谱和Fredholm指标．     

圆环上的Dirichlet空间及其算子

本文主要讨论了圆环上Dirichlet空间中Toeplitz算子的Fredholm性质,计算了符号在C~1和H_1~∞+C~1中的Toeplitz算子的本性谱.     

正整数阶Bergman-Sobolev空间上的Toeplitz算子

单位圆盘上的Bergman-Sobolev空间上的Toeplitz算子比Hardy空间和Bergman空间复杂许多,很多基本问题都有待解决.本文刻画了正整数阶Bergman-Sobolev空间上的Toeplitz算子的有界性、紧性和Fredholm性质.     

H2(Bn)上的Toeplitz算子与复合算子

给出H²(B_n)上复合算子具有闭值域的特征,讨论了Toeplitz算子与复合算子的Fredholm性质。     

有界多连通域的具分段连续符号的Toeplitz算子

探讨多连通域的Bergman空间上的具有分段连续符号的Toeplitz算子,刻画了它们的本质谱和Fredholm指标.     

Toeplitz算子Fredholm性质的局部化描述

利用Banach代数中的局部化定理描述Bergman空间上Toeplitz算子的Fredholm性质,证明了类似于Hardy空间上的一个局部化定理．讨论了L∞（D）的极大理想空间的一些性质．     

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.     

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.     

Algebraic Properties of Toeplitz Operators on the Harmonic Dirichlet Space

We study some algebraic properties of Toeplitz operators on the harmonic Dirichlet space of the unit disk. We first give a characterization for boundedness of Toeplitz operators. Next we characterize commuting Toeplitz operators. Also, we study the product problem of when product of two Toeplitz operators is another Toeplitz operator. The corresponding problems for compactness are also studied.     

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.     

单位球上的对偶Toeplitz算子

本文研究了单位球Bergman空间的直交补上的对偶Toeplitz算子的代数性质,首先我们给出了对偶Toeplitz算子的有界性和紧性的完全刻画,然后给出对偶Toeplitz算子的谱性质,最后证明了不存在以有界全纯或者反全纯函数为符号的拟正规对偶Toeplitz算子.     

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.     

Dual Toeplitz operators on the sphere

Dual Toeplitz operators on the Hardy space of the unit circle are anti-unitarily equivalent to Toeplitz operators. In higher dimensions, for instance on the unit sphere, dual Toeplitz operators might behave quite differently and, therefore, seem to be a worth studying new class of Toeplitz-type operators. The purpose of this paper is to introduce and start a systematic investigation of dual Toeplitz operators on the orthogonal complement of the Hardy space of the unit sphere in Cn . In particular, we establish a corresponding spectral inclusion theorem and a Brown-Halmos type theorem. On the other hand, we characterize commuting dual Toeplitz operators as well as normal and quasinormal ones.     

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.     

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.     

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.