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．     

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.     

多圆盘上的本质交换对偶Toeplitz算子

在单位多圆盘的Bergman空间上,本文分别刻画了以有界可测函数和有界多重调和函数为符号的本质交换对偶Toeplitz算子.     

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.     

带有调和符号的交换Toeplitz算子

我们研究作用于调和Bergman空间b²(D{0})上的带有调和符号的Toeplitz算子,其中D是复平面上的单位圆盘.首先,研究b^p(Ω)的结构并且获得b^p(Ω)中的每个元在调和Bergman投影之下的像.其次,证明特殊的Toeplitz算子T_log|w|:b²(D{0})→b²(D/{0})是有界线性算子并获得带有调和或全纯符号的Toeplitz算子与T_log|w|可交换的充分必要条件.第三,我们获得两个带有全纯符号的Toeplitz算子可交换的充分必要条件.第四,给出带有全纯符号的正规Toeplitz算子的一个特征.最后,得到带有调和符号的Toeplitz算子彼此之间可交换的一个必要条件.     

Dirichlet空间上的Bergman型Toeplitz算子

证明了在Dirichlet空间上以有界调和函数φ为符号的Bergman-型Toeplitz算子T_φ是紧算子的充分必要条件是其符号φ为0;如果φ是单位圆盘D上的连续函数,那么T_φ是紧算子的充分必要条件是φ在D的边界上为0.我们还讨论了此类Toeplitz算子的半换位子.     

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...     

Dirichlet空间上Toeplitz算子的亚正规性

讨论单位圆盘中Dirichlet空间上Toeplitz算子的性质,给出了Dirichiet空间上以一类连续函数为符号的Toeplitz算子满足亚正规性的充分必要条件．     

H~2(T~n)上的可换Toeplitz算子

本文获得了ploydisk上的Hardy空间H2（Tn）上的两个具有多重调和函数符号的Toeplitz算子可换的充要条件由此得出Bergman空间La2（Dn）上的坐标乘子组不能与Hardy空间H2（Tm）上的具有多重调和符号的Toeplitz算子组联合酉等价．     

高维加权Bergman空间上的Toeplitz算子

本文研究了高维加权Bergman空间Ap(Bn,dVpφ)(1＜p＜∞).上的Toeplitz算子.利用Toeplitz算子的Berezin变换,获得了Ap(Bn,dVp)(1＜p＜∞)上具有L∞(Bn)符号的Toeplitz算子的有限乘积的有限和是紧算子的一些等价刻画,推广了加权Bergman空间Ap(D,dmpφ)上的Toeplitz算子的有限乘积的有限和是紧的当且仅当它的Berezin变换在单位圆盘的边界消失为0的结论     

加权Bergman空间上解析Toeplitz算子的换位及相似

本文在加权Bergman 空间A_α²(D)(α>-1) 上证明了由n-Blaschke 因子诱导的解析Toeplitz算子相似于n个Bergman 移位的直接和, 刻画了一类解析Toeplitz 算子的换位并研究了两个解析Toeplitz 算子的相似性.     

多圆盘的加权Bergman空间上的不变子空间和约化子空间

本文主要研究多圆盘的加权Bergman 空间上的不变子空间和约化子空间, 给出了某些解析Toeplitz 算子的极小约化子空间的完全刻画, 以及一类解析Toeplitz 算子Tzi (1≤i≤n) 的不变子空间的Beurling 型定理.     

Dirichlet型空间上Toeplitz算子的本性范数

本文研究单位圆盘上Dirichlet型空间非紧Toeplitz算子的本性范数, 它事实上等于到紧Toeplitz算子集的距离. 并且这个距离可由无限多个紧Toeplitz算子来刻画, 这个结果与加权Bergman空间情形的类似.     

Toeplitz Operators on Arveson and Dirichlet Spaces

We define Toeplitz operators on all Dirichlet spaces on the unit ball of and develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive symbols in terms of Carleson measures and Berezin transforms. Our results naturally extend those known for weighted Bergman spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting case; thus we unify the theory of Toeplitz operators on all these spaces. We apply our operators to a characterization of bounded, compact, and Schatten-class weighted composition operators on weighted Bergman spaces of the ball. We lastly investigate some connections between Toeplitz and shift operators. The research of the second author is partially supported by a Fulbright grant.     

Commutant of analytic Toeplitz operators on the Bergman space

In this paper, we characterize the commutant of Toeplitz operators on weighted Bergman space with symbol polynomial by using algebraic curves theory.     

Invertibility of Bergman Toeplitz operators with harmonic polynomial symbols

Let p be an analytic polynomial on the unit disk. We obtain a necessary and sufficient condition for Toeplitz operators with the symbol z + p to be invertible on the Bergman space when all coefficients of p are real numbers. Furthermore, we establish several necessary and sufficient, easy-to-check conditions for Toeplitz operators with the symbol z + p to be invertible on the Bergman space when some coefficients of p are complex numbers.     

On C*-Algebras of Toeplitz Operators on the Harmonic Bergman Space

Commutative algebras of Toeplitz operators acting on the Bergman space on the unit disk have been completely classified in terms of geometric properties of the symbol class. The question when two Toeplitz operators acting on the harmonic Bergman space commute is still open. In some papers, conditions on the symbols have been given in order to have commutativity of two Toeplitz operators. In this paper, we describe three different algebras of Toeplitz operators acting on the harmonic Bergman space: The C*-algebra generated by Toeplitz operators with radial symbols, in the elliptic case; the C*-algebra generated by Toeplitz operators with piecewise continuous symbols, in the parabolic and hyperbolic cases. We prove that the Calkin algebra of the first two algebras are commutative, like in the case of the Bergman space, while the last one is not.     

COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL

In this article, we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables. Surprisingly, the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same. Also, some interesting symmetry properties of complex symmetric Toeplitz operators are obtained.