共查询到20条相似文献,搜索用时 15 毫秒
1.
Young Joo Lee 《Journal of Mathematical Analysis and Applications》2009,357(2):504-515
On the Dirichlet space of the unit disk, we consider a class of operators which contain finite sums of products of two Toeplitz operators with harmonic symbols. We give characterizations of when an operator in that class is zero or compact. Also, we solve the zero product problem for products of finitely many Toeplitz operators with harmonic symbols. 相似文献
2.
Dirichlet空间上的Bergman型Toeplitz算子 总被引:1,自引:1,他引:0
本文给出了Dirichlet空间上以有界调和函数为符号的Bergman型Toeplitz算子是紧算子的充要条件.同时刻画了此类Bergman型Toeplitz算子在Dirichlet空间上的交换性. 相似文献
3.
Tao Yu 《Integral Equations and Operator Theory》2010,67(2):163-170
In this paper a decomposition of Sobolev space is obtained. Then we prove that a Toeplitz operator on the Dirichlet space
is compact only when it is the zero operator. For two Toeplitz operators on the Dirichlet space, we obtain the conditions
for that they commute, their product is a Toeplitz operator, and their commutator or semi-commutator has finite rank, respectively. 相似文献
4.
Yong Chen Young Joo Lee Quang Dieu Nguyen 《Integral Equations and Operator Theory》2011,69(2):183-201
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. 相似文献
5.
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. 相似文献
6.
J.J. Duistermaat 《Journal of Mathematical Analysis and Applications》2004,300(1):54-67
We study algebraic properties of Toeplitz operators acting on the Dirichlet space. We first characterize two harmonic symbols of commuting Toeplitz operators. Also, we give characterizations of the harmonic symbol for which the corresponding Toeplitz operator is self-adjoint or an isometry. 相似文献
7.
In this paper we characterize commuting dual Toeplitz operators with harmonic symbols on the orthogonal complement of the Dirichlet space in the Sobolev space. We also obtain the sufficient and necessary conditions for the product of two dual Toeplitz operators with harmonic symbols to be a finite rank perturbation of a dual Toeplitz operator. 相似文献
8.
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. 相似文献
9.
10.
In this paper we study Toeplitz operators on Dirichlet spaces and describe the boundedness and compactness of Toeplitz operators
on Dirichlet spaces. Meanwhile, we give density theorems for Toeplitz operators on Dirichlet spaces
Received December 22,1998, Revised March 27, 2000, Accepted June 27, 2000 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.
13.
本文研究了Dirichlet空间上的Toeplitz算子,部分的回答了文[1]中的问题,给出了关于Dirichlet空间上Toeplitz算子的一个稠密性定理。 相似文献
14.
Young Joo Lee 《Journal of Mathematical Analysis and Applications》2007,329(2):1316-1329
We study some algebraic properties of Toeplitz operators on the Dirichlet space. We first characterize (semi-)commuting Toeplitz operators with harmonic symbols. Next we study the product problem of when product of two Toeplitz operators is another Toeplitz operator. As an application, we show that the zero product of two Toeplitz operators with harmonic symbol has only a trivial solution. Also, the corresponding compact product problem is studied. 相似文献
15.
Lian Kuo Zhao 《数学学报(英文版)》2012,28(5):1033-1040
In this paper, we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space, and show that the product
of two Toeplitz operators is another Toeplitz operator only if one factor is constant. 相似文献
16.
Yong Chen 《Journal of Mathematical Analysis and Applications》2009,357(1):214-224
In this paper, we study the commutativity of Toeplitz operators with continuous symbols on the Dirichlet space. First, under a mild condition concerning absolute continuity we characterize (semi-)commuting Toeplitz operators. This is a generalization of the case of harmonic symbols. Also, if one of the symbol is radial or analytic, we get another characterization, which is different from the case on the Bergman space. 相似文献
17.
Tao Yu 《Journal of Mathematical Analysis and Applications》2009,357(1):300-306
In this paper we prove that a dual Hankel operator is zero if and only if its symbol is orthogonal to the Dirichlet space in the Sobolev space, and characterize the symbols for (semi-)commuting dual Toeplitz operators on the orthogonal complement of the Dirichlet space in Sobolev space. 相似文献
18.
In this paper, we completely characterize the compactness of Toeplitz operators with continuous symbol on the weighted Dirichlet space. 相似文献
19.
A celebrated theorem of Coburn asserts that, on the setting of the Hardy space, if a Toeplitz operator is nonzero, then either it is one-to-one or its adjoint operator is one-to-one. In this paper, we show that an analogous result holds for Toeplitz operators acting on the Dirichlet space. 相似文献
20.
On the Bergman space of the unit polydisk, we study a class of operators which contains sums of finitely many Toeplitz products
with pluriharmonic symbols. We give characterizations of when an operator in that class has finite rank or is compact. As
one of applications we show that sums of a certain number, depending on and increasing with the dimension, of semicommutators
of Toeplitz operators with pluriharmonic symbols cannot be compact without being the zero operator. 相似文献