A^p（φ）上的Toeplitz算子与Berezin变换

讨论了加权Bergman空间A^p(φ）（1＜p＜∞）上的Toeplitz算子的有限乘积的有限和是紧算子当且仅当其Berezin变换在边界趋向于零。     

A~p()上的Toeplitz算子与Berezin变换

讨论了加权Bergman空间AP（）（1＜p＜∞）上的Toeplitz算子证明了Toeplitz算子的有限乘积的有限和是紧算子当区仅当其Berezin变换在边界趋向于零．     

加权Bergman空间上Toeplitz算子的本质谱

本文探讨加权Bergman空间Ap(φ)上Toeplitz算子,刻画了L∞(D)的使得符号在其中的Toeplitz算子的半换位子是紧算子的最大的自伴子代数Q,并计算了符号在Q中的Toeplitz算子的本质谱和Fredholm指标．     

单位球上加权Bergman空间的复合型算子

本文给出了Cn中单位球上加权Bergman空间Apα到Bloch型空间βq的加权复合算子Tψ,φ为有界算子和紧算子的简捷充要条件,同时给出了如下结果:(1)若复合算子Cφ在Apα上有界,则Cφ在Apα上紧的充要条件是lim|z|→1-1-|z|/1-|φ(z)|=0.该结果改进了Zhu的相应结果.(2)复合算子Cφ是Apα到βn+1+α+p/p紧算子的充要条件是lim|z|→1-1-|z|/1-|φ(z)|=0.     

Bergman空间上的斜Toeplitz算子

本文讨论了Bergman空间上斜Toeplitz算子的若干性质,证明了:如果线性算子S在每个Lap(1相似文献   

加权Bergman空间上的解析Toeplitz算子的约化子空间

证明了加权Bergman空间上以有限Blaschke乘积φ为符号的解析Toeplitz算子Bφ至少存在一个约化子空间M,并且Bφ在M上的的限制酉等价于加权Bergman位移.     

有界对称区域上Dirichlet空间中的紧Toeplitz算子

介绍了有界对称区域Ω上Dirichlet空间中的Toeplitz算子的紧性:如果S是有限个Toeplitz算子乘积的有限和,S是紧算子当且仅当S的Berezin变换S(z)趋于0.     

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.     

单位球上Bergman空间的Cesàro算子

对一切p∈(0,∞),Cesàro算子在加权的p次Bergman空间Apψ(Bn)上有界,但不是紧的,其中Bn是Cn上中的单位球,而ψ是[0,1)上的正规权函数.与Cesàro算子相联系,以解析函数g为符号的积分算子Rg定义为Rgf→∫z1/0…∫zn/0/f(z1,z2,…,zn)g(z1,z2,…,zn)dz1dz2…dzn.本文刻画了使算子Rg在Apψ(Bn)上是有界(或紧)的解析函数9的特征.同时,在多圆柱上也能得出类似的结果.     

Dirichlet空间上的紧算子

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.     

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．     

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.     

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.     

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.     

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．     

Quasi-Radial Quasi-Homogeneous Symbols and Commutative Banach Algebras of Toeplitz Operators

We present here a quite unexpected result: Apart from already known commutative C*-algebras generated by Toeplitz operators on the unit ball, there are many other Banach algebras generated by Toeplitz operators which are commutative on each weighted Bergman space. These last algebras are non conjugated via biholomorphisms of the unit ball, non of them is a C*-algebra, and for n = 1 all of them collapse to the algebra generated by Toeplitz operators with radial symbols.     

Commutative Toeplitz Banach Algebras on the Ball and Quasi-Nilpotent Group Action

Studying commutative C*-algebras generated by Toeplitz operators on the unit ball it was proved that, given a maximal commutative subgroup of biholomorphisms of the unit ball, the C*-algebra generated by Toeplitz operators, whose symbols are invariant under the action of this subgroup, is commutative on each standard weighted Bergman space. There are five different pairwise non-conjugate model classes of such subgroups: quasi-elliptic, quasi-parabolic, quasi-hyperbolic, nilpotent and quasi-nilpotent. Recently it was observed in Vasilevski (Integr Equ Oper Theory. 66:141–152, 2010) that there are many other, not geometrically defined, classes of symbols which generate commutative Toeplitz operator algebras on each weighted Bergman space. These classes of symbols were subordinated to the quasi-elliptic group, the corresponding commutative operator algebras were Banach, and being extended to C*-algebras they became non-commutative. These results were extended then to the classes of symbols, subordinated to the quasi-hyperbolic and quasi-parabolic groups. In this paper we prove the analogous commutativity result for Toeplitz operators whose symbols are subordinated to the quasi-nilpotent group. At the same time we conjecture that apart from the known C*-algebra cases there are no more new Banach algebras generated by Toeplitz operators whose symbols are subordinated to the nilpotent group and which are commutative on each weighted Bergman space.     

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.