Bergman空间上拟齐次Toeplitz算子的乘积

使用Mellin变换作为工具,讨论了Bergman空间上以拟齐次函数为符号的Toeplitz算子的乘积问题,得出了当拟齐次函数的度处于三种不同情况时两个Toeplitz算子乘积仍是Toeplitz算子的充分必要条件.     

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.     

加权Bergman空间上的Toeplitz算子和Hankel算子

西方给出了Ｃ＾ｎ中单位球上的带权的Ｂｅｒｇｍａｎ空间上具一般符号的Ｔｏｅｐｌｉｔｚ算子和Ｈａｎｋｅｌ算子为紧的充要条件。     

Bergman空间上Toeplitz算子的局部化

Bergman空间上Toeplitz算子的局部化@孙善利@卢玉峰...     

多圆柱上的Bloch空间上的紧复合算子

设Un是n维复空间Cⁿ中的单位多圆柱.若φ是Uⁿ到自身的一个全纯映射,则复合算子C_φ在β(Uⁿ)紧的充要条件是对任意的ε>0,存在δ>0,使得对任意的z∈Uⁿ,当dist(φ(z),¶Uⁿ)<δ时,     

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.     

Bergman空间上的斜Toeplitz算子

本文讨论了Bergman空间上斜Toeplitz算子的若干性质,证明了:如果线性算子S在每个Lap(1相似文献   

Bergman空间上Toeplitz算子的迹理想刻划

本文给出了C~n内单位球的加权Bergman空间上,以测度为符号的Toeplitz算子属于Schatten p-类(0相似文献   

Bergman空间上Toeplitz算子的凸性

本文讨论了Ｂｅｒｇｍａｎ空间上Ｔｏｅｐｌｉｔｚ算子的凸性，证明了具有调和符号和一类连续函数符号的Ｔｏｅｐｌｉｔｚ算子是凸型算子，并举例说明，存在具有连续函数符号的非凸型Ｔｏｅｐｌｉｔｚ算子。     

单位圆盘加权Bergman空间上Toeplitz算子的本性范数

对于D上的Carleson测度μ而言,本文研究在加权Bergman空间Aα~2（D）上具有符号μ的Toeplitz算子Tμ的一些特殊的性质.近几年,在加权Bergman空间Aα~2（D）上的Toeplitz算子的有界性和紧性已经被广泛研究.为了了解Toeplitz算子Tμ的一些其他性质,本文需要估算出单位圆盘的加权Bergman空间上Toeplitz算子的本性范数的界限.     

Finite rank Toeplitz operators on the Bergman space

Given a complex Borel measure with compact support in the complex plane the sesquilinear form defined on analytic polynomials and by , determines an operator from the space of such polynomials to the space of linear functionals on . This operator is called the Toeplitz operator with symbol . We show that has finite rank if and only if is a finite linear combination of point masses. Application to Toeplitz operators on the Bergman space is immediate.

     

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.

     

Algebraic properties of Toeplitz and small Hankel operators on the harmonic Bergman space

In this paper,we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C.We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.Meanwhile,we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.     

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.

     

多重调和Bergman空间上的Toeplitz算子和Hankel算子

完全刻画多重调和Bergman空间上Toeplitz算子和Hankel算子的紧性.运用紧Toeplitz算子这个结果,建立了Toeplitz代数和小Hankel代数的短正合列,推广了单位圆盘上相应的结果.     

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.     

A question of Toeplitz operators on the harmonic Bergman space

Choe and Lee [B.R. Choe, Y.J. Lee, Commuting Toeplitz operators on the harmonic Bergman space, Michigan Math. J. 46 (1999) 163-174] put the question: If an analytic Toeplitz operator and a co-analytic Toeplitz operator on the harmonic Bergman space commute, then is one of their symbols constant? If one of their symbols is bounded, then we will show that the answer is yes.     

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.     

The commutant of analytic Toeplitz operators on Bergman space

In this paper, using the matrix skills and operator theory techniques we characterize the commutant of analytic Toeplitz operators on Bergman space. For f（z） = z^ng（z） （n ≥1）, g（z） = b0 ＋ b1z^p1 ＋b2z^p2 ＋.. , bk ≠ 0 （k = 0, 1, 2,...）, our main result is =A′（Mf） = A′（Mzn）∩A′（Mg） = A′（Mz^s）, where s = g.c.d.（n,p1,p2,...）. In the last section, we study the relation between strongly irreducible curve and the winding number W（f,f（α））, α ∈ D.