Positive Schatten(-Herz) Class Toeplitz Operators on Pluriharmonic Bergman Spaces

We study characterizations of arbitrary positive Toeplitz operators of Schatten (or Schatten-Herz) type in terms of averaging functions and Berezin transforms of symbol functions on the ball of pluriharmonic Bergman space. This work was supported by a Hanshin University Research Grant.     

Ap(φ)上Toeplitz算子的半换位子

本文给出加权Bergman空间A^p(φ)上具有界调和符号的Toeplitz算子的半换位子为零或为紧算子的一些充要条件.     

Ap(ψ)上Toeplitz算子的半换位子

本文给出加权Bergman空间Ap(ψ)上具有界调和符号的Toeplitz算子的半换位子为零或为紧算子的一些充要条件.     

多复变Bergman空间上坐标乘子组的联合酉等价性

本文讨论多复变Ｂｅｒｇｍａｎ空间上坐标乘子组联合酉等价的条件以及与多复变Ｈａｒｄｙ空间上Ｔｏｅｐｌｉｔｚ算子组的关系     

Toeplitz Operators with Special Symbols on Segal–Bargmann Spaces

We study the boundedness of Toeplitz operators on Segal–Bargmann spaces in various contexts. Using Gutzmer’s formula as the main tool we identify symbols for which the Toeplitz operators correspond to Fourier multipliers on the underlying groups. The spaces considered include Fock spaces, Hermite and twisted Bergman spaces and Segal–Bargmann spaces associated to Riemannian symmetric spaces of compact type.     

A^p（φ）上Toeplitz算子的换位子

本文使用不变加权面积平均值性质刻画了单位圆盘内的调和函数．由此我们探讨了加权Bergman空间A^p(φ)上的Toeplitz算子，给出了两个具有界调和符号的Toeplitz算子交换或本质交换的一些充要条件．     

Ap(ψ)上Toeplitz算子的换位子

本文使用不变加权面积平均值性质刻画了单位圆盘内的调和函数.由此我们探讨了加权Bergman空间Ap(ψ)上的Toeplitz算子,给出了两个具有界调和符号的Toeplitz算子交换或本质交换的一些充要条件.     

COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL

In this article, we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables. Surprisingly, the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same. Also, some interesting symmetry properties of complex symmetric Toeplitz operators are obtained.     

加权Bergman空间上的Toeplitz算子和Hankel算子

西方给出了Ｃ＾ｎ中单位球上的带权的Ｂｅｒｇｍａｎ空间上具一般符号的Ｔｏｅｐｌｉｔｚ算子和Ｈａｎｋｅｌ算子为紧的充要条件。     

Commuting dual Toeplitz operators on weighted Bergman spaces of the unit ball

In this paper, we study the commutativity of dual Toeplitz operators on weighted Bergman spaces of the unit ball. We obtain the necessary and sufficient conditions for the commutativity, essential commutativity and essential semi-commutativity of dual Toeplitz operator on the weighted Bergman spaces of the unit ball.     

Operators on harmonic Bergman spaces

We study the commutator of the multiplication and harmonic Bergman projection, Hankel and Toeplitz operators on the harmonic Bergman spaces. The same type operators have been well studied on the analytic Bergman spaces. The main difficulty of this study is that the bounded harmonic function space is not an algebra! In this paper, we characterize theL ^p boundedness and compactness of these operators with harmonic symbols. Results about operators in Schatten classes, the cut-off phenomenon and general symbols are also included.Partially supported by a grant from the Research Grants Committee of the University of Alabama.     

Toeplitz Operators on Arveson and Dirichlet Spaces

We define Toeplitz operators on all Dirichlet spaces on the unit ball of and develop their basic properties. We characterize bounded, compact, and Schatten-class Toeplitz operators with positive symbols in terms of Carleson measures and Berezin transforms. Our results naturally extend those known for weighted Bergman spaces, a special case applies to the Arveson space, and we recover the classical Hardy-space Toeplitz operators in a limiting case; thus we unify the theory of Toeplitz operators on all these spaces. We apply our operators to a characterization of bounded, compact, and Schatten-class weighted composition operators on weighted Bergman spaces of the ball. We lastly investigate some connections between Toeplitz and shift operators. The research of the second author is partially supported by a Fulbright grant.     

Bergman空间上Toeplitz算子的局部化

In this paper we characterize the essential spectra of Toeplitz operators on Bergman spaces by using Douglas‘ localization Theorem and obtain the local decomposition of the essential spectra of Toeplitz operators.     

Positive Schatten(-Herz) Class Toeplitz Operators on the Half-space

On the harmonic Bergman space of the half-space, we give characterizations for an arbitrary positive Toeplitz operator to be a Schatten (or Schatten-Herz) class operator in terms of averaging functions and Berezin transforms. Examples are provided to show that various results are sharp. This research was supported by KOSEF(R01-2003-000-10243-0).     

Discretizations of Integral Operators and Atomic Decompositions in Vector-Valued Weighted Bergman Spaces

We prove a general atomic decomposition theorem for weighted vector-valued Bergman spaces, which applies to duality problems and to the study of compact Toeplitz type operators.      

Maximal Abelian von Neumann Algebras and Toeplitz Operators with Separately Radial Symbols

This paper mainly concerns abelian von Neumann algebras generated by Toeplitz operators on weighted Bergman spaces. Recently a family of abelian w^*-closed Toeplitz algebras has been obtained (see [5,6,7,8]). We show that this algebra is maximal abelian and is singly generated by a Toeplitz operator with a “common” symbol. A characterization for Toeplitz operators with radial symbols is obtained and generalized to the high dimensional case. We give several examples for abelian von Neumann algebras in the case of high dimensional weighted Bergman spaces, which are different from the one dimensional case.     

加权Bergman空间上的紧算子

本文讨论了加权Ｂｅｒｇｍａｎ空间上的Ｔｏｅｐｌｉｔｚ算子,证明了Ｔｏｐｌｉｔｚ算子的有限乘积的有限和是紧的当且仅当它的Ｂｅｒｅｚｉｎ变换在边界上趋向于零．     

Irreducibility of Toeplitz C⋆-algebras

We probe the irreducibility of the Toeplitz C^*-algebras generated by Toeplitz operators on Bergman and Hardy spaces associated with generalized upper half-planes in several complex variables.     

Fejér–Riesz type inequalities for Bergman spaces

We obtain Fejér?CRiesz type inequalities for the weighted Bergman spaces on the unit disk of the complex plane. We show that the Fejér?CRiesz inequalities can be expressed as boundedness and compactness problems for certain Toeplitz operators.     

Composition operators on weighted Dirichlet spaces

We characterize bounded and compact composition operators on weighted Dirichlet spaces. The method involves integral averages of the determining function for the operator, and the connection between composition operators on Dirichlet spaces and Toeplitz operators on Bergman spaces. We also present several examples and counter-examples that point out the borderlines of the result and its connections to other themes.