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.     

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.     

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Hardy空间上的Berezin变换和Toeplitz算子的交换性

,该文讨论多圆盘上Hardy空间上的Toeplitz算子,使用Berezin变换和调和扩张给出两个Toeplitz算子交换的一个充要条件.     

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.     

单位多圆盘加权Bergman空间上Toeplitz算子的本质谱

本文研究了单位多圆盘加权Bergman空间AΦp(Dn)上的Toeplitz算子.利用多圆盘函数论,获得了L∞(Dn)的使得符号在其中的Toeplitz算子的半换位子是紧算子的最大自伴子代数Q,并计算了符号在Q中的Toeplitz算子的本质谱.     

多圆盘上对偶Toeplitz算子的性质

本文研究了多圆盘上对偶Toeplitz算子的有界性、紧性和谱的特征。     

多圆盘上的交换对偶Toeplitz算子

We completely characterize commutativity of Sρ and Sψ on L2α (Dn)⊥ for bounded pluriharmonic symbols ρ and ψ on Dn, and prove that SρSψ=Sψρ if and only if ρ is analytic or ψ is analytic.     

多复变量Toeplitz算子的交换性

本文刻画了Cn中单位球和多圆盘Bergman空间上一些Toeplitz算子的换位.首先,对双圆盘Bergman空间,刻画了什么时候Toeplitz算子Tf和Tg交换,这里f=f1+-f2,g=g1+-g2,fi,gi∈H∞(D2)(i=1,2).其次,如果R表示由多复变量Toeplitz算子生成的赋范闭子代数,证明了对每个正整数m,{Tzm,…,Tzmn}'∩R是所有解析Toeplitz算子的集合,这里zi(i=1,…,n)是坐标函数.     

多复变量Toeplitz算子的交换性

本文刻画了C~n中单位球和多圆盘Bergman空间上一些Toeplitz算子的换位。首先,对双圆盘Bergman空间,刻画了什么时候 Toeplitz算子T_f和T_g交换,这里 f=f1+,g=g1+,fi,gi∈H~∞(D~2)(i=1,2)。其次,如果表示由多复变量 Toeplitz算子生成的赋范闭子代数,证明了对每个正整数m,{T_z_1~m,…,T_z_n~m}′∩是所有解析Toeplitz算子的集合,这里z_i(i=1,…,n)是坐标函数。     

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.     

Toeplitz operators on the polydisk

In this paper it is shown that two analytic Toeplitz operators essentially doubly commute if and only if they doubly commute on the Bergman space of the polydisk.

     

Invertible Toeplitz Operators Products on the Bergman Space of the Polydisk

We prove a reverse Hlder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk.Next,we further describe when for which square integrable analytic functions f and g on the polydisk the densely defined products Tf Tg are bounded invertible Toeplitz operators.     

多元盘Bergman空间上可逆的Toeplitz算子乘积

We prove a reverse Hlder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk.Next,we further describe when for which square integrable analytic functions f and g on the polydisk the densely defined products Tf Tg are bounded invertible Toeplitz operators.     

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.     

Bergman空间上可交换的Hankel算子和Toeplitz算子

证明了Bergman空间上的两个小Hankel算子如果是可交换的且其中一个是拟齐次的小Hankel算子,则另一个也是拟齐次的.还研究了Toeplitz算子和小Hankel算子的交换性.     

Commuting Toeplitz operators on the polydisk

We obtain characterizations of (essentially) commuting Toeplitz operators with pluriharmonic symbols on the Bergman space of the polydisk. We show that commuting and essential commuting properties are the same for dimensions bigger than 2, while they are not for dimensions less than or equal to 2. Also, the corresponding results for semi-commutators are obtained.