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1.
For the unilateral shift operator U on the Hardy space H2(T), we describe conditions on operators T, acting on H2(T), that are necessary and sufficient for the pair (U, T) to be jointly hyponormal. One necessary condition is that T be a Toeplitz operator. Consequently, we study certain nonanalytic symbols that give rise to Toeplitz operators hyponormal with the shift, and thereby obtain examples of noncommuting, jointly hyponormal pairs.Supported in part by a research grant from NSERC 相似文献
2.
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
3.
本文讨论了Fock空间上以径向函数和拟齐次函数为符号的Toeplitz算子的代数性质,给出了两个以径向函数为符号的Toeplitz算子的积仍为Toeplitz算子的充分必要条件,并且研究了以拟齐次函数为符号的Toeplitz算子的交换性. 相似文献
4.
5.
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
6.
Gerard J. Murphy 《Integral Equations and Operator Theory》1997,27(4):439-445
An aspect of the theory of Toeplitz operators on generalised Hardy spaces is considered, namely, a necessary and sufficient condition on the symbols to ensure that the product of two Toeplitz operators is itself a Toeplitz operator. The answer to this question draws on many deep results of the theory of generalised Hardy spaces. 相似文献
7.
We study the commuting problem for Toeplitz operators on the harmonic Bergman space of the unit disk. We show that an analytic Toeplitz operator and a co-analytic Toeplitz operator with certain noncyclicity hypothesis can commute only when one of their symbols is constant. We also obtain analogous results for semi-commutants. 相似文献
8.
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. 相似文献
9.
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
10.
研究多重调和Bergman空间上的Topelitz算子.对多重调和符号的Topelitz算子,给出了乘积性质、交换性质的符号描述. 相似文献
11.
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
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.
Toeplitz operators on Dirichlet spaces 总被引:13,自引:0,他引:13
In this paper we consider Toeplitz operators on Dirichlet spaces of the unit disk in whose symbols are nonnegative measures. We obtain necessry and sufficient conditions on the symbols for the operator to be bounded and compact. If the symbols are supported in a cone we also get necessary and sufficient conditions for the operators to belong to the Schatten p-class. Application to the Hankel operators are indicated.This work supported in part by NSF grant DMS 8701271 相似文献
14.
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
15.
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
16.
17.
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. 相似文献
18.
A. Böttcher S. Grudsky I. Spitkovsky 《Journal of Fourier Analysis and Applications》2001,7(5):523-535
It is well known that amplitude modulation does not affect Fredholmness of Toeplitz operators. The same is true for frequency
modulation provided the symbol of the operator is piecewise continuous. In this article, it is shown that frequency modulation
can destroy Fredholmness for Toeplitz operators with almost periodic symbols; the corresponding example is based on the observation
that certain almost periodic functions become semi-almost periodic functions after appropriate frequency modulation. Moreover,
this article contains several results that can be employed in order to decide whether a Toeplitz operator with a frequency
modulated semi-almost periodic symbol is Fredholm. 相似文献
19.
The commutant and similarity invariant of analytic Toeplitz operators on Bergman space 总被引:1,自引:0,他引:1
The famous von Neumann-Wold Theorem tells us that each analytic Toeplitz operator with n 1-Blaschke factors is unitary to n 1 copies of the unilateral shift on the Hardy space. It is obvious that the von Neumann-Wold Theorem does not hold in the Bergman space. In this paper, using the basis constructed by Michael and Zhu on the Bergman space we prove that each analytic Toeplitz operator Mb(z) is similar to n 1 copies of the Bergman shift if and only if B(z) is an n 1-Blaschke product. Prom the above theorem, we characterize the similarity invariant of some analytic Toeplitz operators by using K0-group term. 相似文献
20.
In this paper, we study the commutativity of Toeplitz operators with radial symbols on the pluriharmonic Bergman space. We obtain the necessary and sufficient conditions for the commutativity of bounded Toeplitz operator and Toeplitz operator with radial symbol on the pluriharmonic Bergman space. 相似文献