共查询到18条相似文献,搜索用时 62 毫秒
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A^p(φ)上的Toeplitz算子与Berezin变换 总被引:1,自引:0,他引:1
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。 相似文献
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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. 相似文献
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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. 相似文献
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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. 相似文献
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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. 相似文献
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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. 相似文献
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加权Bergman空间上的紧算子 总被引:2,自引:0,他引:2
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. 相似文献
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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. 相似文献
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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. 相似文献
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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. 相似文献
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Nikolai Vasilevski 《Integral Equations and Operator Theory》2010,66(1):141-152
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. 相似文献
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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. 相似文献
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本文给出加权Bergman空间Ap(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. 相似文献