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1.
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
2.
In this paper we investigate some algebra properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space in the Sobolev space. We completely characterize commuting dual Toeplitz operators with harmonic symbols, and show that a dual Toeplitz operator commutes with a nonconstant analytic dual Toeplitz operator if and only if its symbol is analytic. We also obtain the sufficient and necessary conditions on the harmonic symbols for SφSφψ= Sφψ. 相似文献
3.
研究对偶Toeplitz算子(半)交换时其符号的关系.通过对其符号的分解,借助多复变函数的有关理论,得到了单位球Dirichlet空间上以多重调和函数为符号的对偶Toeplitz算子Sψ与Sψ(半)交换的充要条件. 相似文献
4.
In this paper,we characterize the symbols for(semi-)commuting dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space.We show that for φ,ψ∈W~(1,∞),S_φS_ψ=S_ψ Sφ on(D_h)~⊥ if and only if φ and ψ satisfy one of the following conditions:(1) Both φ and ψ are harmonic functions;(2) There exist complex constants α and β,not both 0,such that φ=αψ +β. 相似文献
5.
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
6.
Dirichlet空间上Toeplitz算子的紧性 总被引:1,自引:0,他引:1
本文给出了 Dirichlet空间上 Toelpitz算子为紧算子的充要条件,并证明具有 C1-符号的 Toeplitz算子为紧算子当且仅当它为零算子,当且仅当符号的边值为零. 相似文献
7.
In this paper,we prove that the necessary and sufficient condition for a Toeplitz operator Tu on the Dirichlet space to be hyponormal is that the symbol u is constant for the case that the projection of u in the Dirichlet space is a polynomial and for the case that u is a class of special symbols,respectively.We also prove that a Toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant. 相似文献
8.
In this paper, we study some algebraic and spectral properties of dual Toeplitz operators on the orthogonal complement of the harmonic Dirichlet space of the unit disk. 相似文献
9.
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
10.
11.
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
12.
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
13.
Liankuo Zhao 《Journal of Mathematical Analysis and Applications》2009,352(2):767-772
We study (small) Hankel operators on the Dirichlet space D with symbols in a class of function space, and show that such (small) Hankel operators are closely related to the corresponding Hankel operators on the Bergman space and the Hardy space H2. 相似文献
14.
In this paper, we completely characterize the compactness of Toeplitz operators with continuous symbol on the weighted Dirichlet space. 相似文献
15.
On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. Based on this, we characterize when finite sums of products of Toeplitz operators are of finite rank. Also, we give a necessary and sufficient condition for the commutator and semi-commutator of two Toeplitz operators being zero. 相似文献
16.
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
17.
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
18.
若S是Dirichlet空间上有限个Toeplitz算子乘积的有限和, S为紧算子的充要条件是: 当z→∂D时, S的Berezin型变换收敛到0; 若S是Dirichlet空间上Hankel算子, S为紧算子的充要条件是: 当z→ D时, S作用在类再生核上按范数收敛到0. 相似文献
19.
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