共查询到17条相似文献,搜索用时 93 毫秒
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丁宣浩 《数学年刊A辑(中文版)》2013,34(1):81-86
截断调和Bergman空间b_n~2=L_a~2{w,w~2,…,w~n}~v是Hilbert空间L~2的闭子空间.研究了单位圆盘上的截断调和Bergman空间上的Toeplitz算子的乘积问题,完整地刻画了具有有界调和符号的两个Toeplitz算子的有限秩与紧的半换位子或换位子. 相似文献
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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
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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
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研究了与强奇异Calder\'{o}n-Zygmund算子和加权
Lipschitz函数${\rm Lip}_{\beta_0,\omega}$相关的Toeplitz算子$T_b$的sharp极大函数的点态估计,并证明了Toeplitz算子是从
$L^p(\omega)$到$L^q(\omega^{1-q})$上的有界算子.此外, 建立了与强奇异Calder\'{o}n-Zygmund算子和加权
BMO函数${\rm BMO}_{\omega}$相关的Toeplitz算子$T_b$的sharp极大函数的点态估计,并证明了Toeplitz算子是从
$L^p(\mu)$到$L^q(\nu)$上的有界算子.上述结果包含了相应交换子的有界性. 相似文献
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探讨了C^n中单位球面S上Berezin变换和Toeplitz算子的性质,证明了由{Tφ,φ∈L^∞ (S)}所生成的C^*-代数中算子T的符号恰好为单位球B上函数T(称为T的Berezin变换)的非切向边界值.此外,本文还得到了经典Toeplitz符号演算的有趣推广. 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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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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In this paper,we construct a function φ in L2(Cn,d Vα) which is unbounded on any neighborhood of each point in Cnsuch that Tφ is a trace class operator on the SegalBargmann space H2(Cn,d Vα).In addition,we also characterize the Schatten p-class Toeplitz operators with positive measure symbols on H2(Cn,d Vα). 相似文献
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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
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Issam Louhichi 《Proceedings of the American Mathematical Society》2007,135(5):1465-1475
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 .
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Algebraic Properties of Toeplitz Operators with Radial Symbols on the Bergman Space of the Unit Ball
In this paper, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Bergman space of the
unit ball in . We first determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator. Next, we investigate
the zero-product problem for several Toeplitz operators with radial symbols. Also, the corresponding commuting problem of
Toeplitz operators whose symbols are of the form is studied, where and φ is a radial function.
Ze-Hua Zhou: supported in part by the National Natural Science Foundation of China (Grand Nos.10671141, 10371091). 相似文献
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In this paper, the product and commutativity of slant Toeplitz operators are discussed. We show that the product of kth1-order slant Toeplitz operators and kth2-order slant Toeplitz operators must be a (k1k2) th-order slant Toeplitz operator except for zero operators, and the commutativity and essential commutativity of two slant Toeplitz operators with different orders are the same. 相似文献
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对于L~(α,2)(D))的两类Moebius不变子空间A~(α,2)(D)和A~(β,2)(D),我们定义了它们之间的Toeplitz算子T_f~s与其乘积空间上的Hankel算子H_f~r,并且研究了它们的有界性、紧性及Schatten-von Neumann性质。 相似文献
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In this paper, we first investigate the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols on the harmonic Bergman space. Next, we characterize finite rank commutators and semi-commutators of two Toeplitz operators with quasihomogeneous symbols. 相似文献