单位球Dirichlet空间上以拟齐次函数为符号的Toeplitz算子

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.     

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.     

The spectrum of Bergman Toeplitz operators with some harmonic symbols

In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and  equals the image of closed unit disk under the symbol.Surprisingly this does not hold for Toeplitz operators with harmonic symbols of quadratic functions of z and .     

Commuting dual Toeplitz operators on the orthogonal complement of the Dirichlet space

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.     

Toeplitz operators on Fock-Sobolev spaces with positive measure symbols

We discuss Toeplitz operators on Fock-Sobolev space with positive measure symbols.By FockCarleson measure,we obtain the characterizations for boundedness and compactness of Toeplitz operators.We also give some equivalent conditions of Schatten p-class properties of Toeplitz operators by Berezin transform.     

TOEPLITZ OPERATORS WITH POSITIVE OPERATOR-VALUED SYMBOLS ON VECTOR-VALUED GENERALIZED FOCK SPACES

In this article, we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces F_φ~2. Main results including Fock-Carleson condition, bounded Toeplitz operators, compact Toeplitz operators, and Toeplitz operators in the Schatten-p class are all considered.     

多重调和Bergman空间上径向Toeplitz算子的交换性

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.     

Algebraic properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space

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.     

Little Hankel Operators on the Weighted Bergman Space of the Unit Ball

In this paper we mainly consider little Hankel operators with squareintegrable symbols on the weighted Bergman spaces of the unit ball.We obtain that Schatten class of little Hankel operators is equivalent to Schatten class of positive Toeplitz operators under the conditions that SMO（f） ∈ L p/2 （B n,dλ） and 2 ≤ p ∞,which is very important to research the relation between Toeplitz operators and little Hankel operators.     

多连通域的Bergman空间上的Toeplitz算子

In this paper, we investigate the Toeplitz operators with positive measure symbols on the Bergman spaces of bounded multi-connected domains and show that a Toeplitz operator is bounded or compact if and only if the symbol measure is a Carleson or vanishing Carleson measure respectively.     

单位多圆柱上Bergman空间中的分别准齐次ToePlitz算子

本文研究了单位多圆柱上Bergman空间中以分别准齐次函数为记号的Toeplitz算子的代数性质.我们首先得到了两个以分别准齐次函数为记号的Toeplitz算子可以写成一个Toeplitz算子的充分必要条件,然后利用L2(Dn,dV)的一个极分解式证明了,只要其中有一个Toeplitz算子是分别准齐次的,则其零乘积问题...     

截断调和Bergman空间上Toeplitz算子的代数性质

本文首先讨论调截断和Bergman空间 $b_{n}^{2}$ 上拟齐次函数为符号的Toeplitz算子的有限秩乘积问题,其次考察两个以拟齐次函数为符号的Toeplitz算子的换位子与半换位子的有限秩问题.     

Commuting Quasihomogeneous Toeplitz Operators on the Harmonic Bergman Space

In this paper, we obtain a symmetry number for the commutator of quasihomogeneous Toeplitz operators on the harmonic Bergman space. Then we use it to characterize the commuting Toeplitz operators with quasihomogeneous symbols. Also, we show that a Toeplitz operator with an analytic or co-analytic monomial symbol commutes with another Toeplitz operator only in the trivial case.     

Finite Rank Commutators and Semicommutators of Quasihomogeneous Toeplitz Operators

We study finite rank semicommutators and commutators of Toeplitz operators on the Bergman space with quasihomogeneous symbols. We show that in this context, the situation is different from the case of harmonic Toeplitz operators. Submitted: July 23, 2007. Accepted: December 4, 2007.     

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.     

Bicommutants of Toeplitz operators

In this paper we discuss an unusual phenomenon in the context of Toeplitz operators in the Bergman space on the unit disc: If two Toeplitz operators commute with a quasihomogeneous Toeplitz operator, then they commute with each other. In the Bourbaki terminology, this result can be stated as follows: The commutant of a quasihomogeneous Toeplitz operator is equal to its bicommutant. Received: 11 March 2008     

Ranks of commutators and generalized semicommutators of quasihomogeneous Toeplitz operators

This paper is devoted to solve the finite rank problem for the commutator and generalized semicommutator of Toeplitz operators with quasihomogeneous symbols acting on both the harmonic Bergman space and the Bergman space. In particular, when one of quasihomogeneous symbols is the form of \(e^{ik\theta }r^{m}\), we first obtain specific sufficient and necessary conditions for the commutator and generalized semicommutator to be finite rank. Then we make further efforts to determine the range of the finite rank commutator and generalized semicommutator, and consequently the rank and the explicit canonical form are obtained. As applications, several interesting corollaries and nontrivial examples are given.     

Powers and roots of Toeplitz operators

We study the commutativity of two Toeplitz operators whose symbols are quasihomogeneous functions. We give a relationship between this commutativity and the roots (or powers) of the Toeplitz operators. We use this to characterize Toeplitz operators with symbols in which commute with Toeplitz operators whose symbols are of the form .