共查询到20条相似文献,搜索用时 15 毫秒
1.
Products of Toeplitz Operators on the Polydisk 总被引:1,自引:0,他引:1
Xuanhao Ding 《Integral Equations and Operator Theory》2003,45(4):389-403
This paper studies products of Toeplitz operators on the Hardy
space of the polydisk. We show that T
f
T
g
= 0 if and only if T
f
T
g
is a finite
rank if and only if T
f
or T
g
is zero. The product T
f
T
g
is still a Toeplitz
operator if and only if there is a h
$ \in $
L
$ \infty $
(T
n
) such that T
f
T
g
- T
h
is a finite
rank operator. We also show that there are no compact simi-commutators
with symbols pluriharmonic on the polydisk.
Submitted: October 5, 2000 相似文献
2.
In this paper, we characterize the compactness and Fredholmness of Toeplitz operators and Toeplitz products on Bergman–Sobolev spaces over the unit polydisk. We also calculate the essential norm of finite sums of finite Toeplitz products on these spaces. 相似文献
3.
We prove a reverse Hlder 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. 相似文献
4.
We prove a reverse Hlder 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. 相似文献
5.
孙志玲 《数学物理学报(A辑)》2020,(2):304-314
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. 相似文献
6.
本文证明了对偶Toeplitz代数${\cal I}(C(\overline{D^n}))$的半换位理想是紧算子全体,并研究了其代数结构,得到了对偶Toeplitz算子的一些谱性质. 相似文献
7.
Commuting Dual Toeplitz Operators on the Polydisk 总被引:1,自引:0,他引:1
Yu Feng LU Shu Xia SHANG 《数学学报(英文版)》2007,23(5):857-868
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. 相似文献
8.
多圆盘上的交换对偶Toeplitz算子 总被引:1,自引:0,他引:1
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. 相似文献
9.
10.
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. 相似文献
11.
On the Dirichlet space of the unit disk, we consider operators that are finite sums of Toeplitz products, Hankel products
or products of a Toeplitz operator and a Hankel operator. We characterize when such operators are equal to zero. Our results
extend several known results using completely different arguments. 相似文献
12.
多圆盘上的Toeplitz算子的紧的乘积 总被引:1,自引:1,他引:0
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. 相似文献
13.
On the weighted Bergman and Dirichlet spaces, we characterize the compactness for operators which are finite sums of products of several Toeplitz operators. Our results extend the several known results by using complete different arguments. 相似文献
14.
15.
The main purpose of this paper is to extend and refine some work of Agler–McCarthy and Amar concerning the Corona problem
for the polydisk and the unit ball in
\mathbbCn\mathbb{C}^n. 相似文献
16.
17.
If A is a finite set of positive integers, letE_h(A) denote the set of h-fold sums andh -fold products of elements of A. This paper is concerned with the behavior of the function f_h(k), the minimum of E_h(A) taken over all A withA=k . Upper and lower bounds for f_h(k) are proved, improving bounds given by Erds, Szemerédi, and Nathanson. Moreover, the lower bound holds when we allow A to be a finite set of arbitrary positive real numbers. 相似文献
18.
对多圆盘上的平方可积函数f和g,研究了Bergman空间上稠密定义的Hankel乘积H_fH_g~*的有界性和紧性.给出了这些算子有界和紧的一些必要条件和充分条件.当f是解析函数时,对混合Haplitz乘积H_gT_(f~-)和T_fH_g~*得到了相似的结果. 相似文献
19.
,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. 相似文献
20.
对多圆盘上的平方可积函数f和g,研究了Bergman空间上稠密定义的Hankel乘积HfH*g的有界性和紧性.给出了这些算子有界和紧的一些必要条件和充分条件.当f是解析函数时,对混合Haplitz乘积HgT-f和TfH*g得到了相似的结果. 相似文献