共查询到19条相似文献,搜索用时 109 毫秒
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本文研究单位圆盘上Dirichlet型空间非紧Toeplitz算子的本性范数, 它事实上等于到紧Toeplitz算子集的距离. 并且这个距离可由无限多个紧Toeplitz算子来刻画, 这个结果与加权Bergman空间情形的类似. 相似文献
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讨论了Dirichlet空间上Toeplitz算子的紧性,特别地得到了Schatlen类Toeplitz算子的特征.此外,还证明了关于Toeplitz算子的一个非稠密性定理,并证明一个非零的函数可以诱导一个零算子,这与Hardy空间及Bergman空间情形是一重大差别. 相似文献
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对于D上的Carleson测度μ而言,本文研究在加权Bergman空间Aα~2(D)上具有符号μ的Toeplitz算子Tμ的一些特殊的性质.近几年,在加权Bergman空间Aα~2(D)上的Toeplitz算子的有界性和紧性已经被广泛研究.为了了解Toeplitz算子Tμ的一些其他性质,本文需要估算出单位圆盘的加权Bergman空间上Toeplitz算子的本性范数的界限. 相似文献
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完全刻画多重调和Bergman空间上Toeplitz算子和Hankel算子的紧性.运用紧Toeplitz算子这个结果,建立了Toeplitz代数和小Hankel代数的短正合列,推广了单位圆盘上相应的结果. 相似文献
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与调和Bergman 空间相对应, 本文研究重调和Hardy 空间h2(D2) 上的Toeplitz 算子. 本文发现, h2(D2) 上的Toeplitz 算子与经典的Hardy 空间、Bergman 空间及调和Bergman 空间上的Toeplitz算子的性质都有很大的差异. 例如解析Toeplitz 算子可以不是半可换及可交换的. 即使半可换, 其中任何一个符号可以不为常数; 即使可交换, 两个符号的非平凡线性组合也不一定是常数. 本文得到了h2(D2) 上两个解析Toeplitz 算子半可换和可换的充分必要条件. 相似文献
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Lian Kuo Zhao 《数学学报(英文版)》2012,28(5):1033-1040
In this paper, we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space, and show that the product
of two Toeplitz operators is another Toeplitz operator only if one factor is constant. 相似文献
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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. 相似文献
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J.J. Duistermaat 《Journal of Mathematical Analysis and Applications》2004,300(1):54-67
We study algebraic properties of Toeplitz operators acting on the Dirichlet space. We first characterize two harmonic symbols of commuting Toeplitz operators. Also, we give characterizations of the harmonic symbol for which the corresponding Toeplitz operator is self-adjoint or an isometry. 相似文献
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Young Joo Lee 《Journal of Mathematical Analysis and Applications》2009,357(2):504-515
On the Dirichlet space of the unit disk, we consider a class of operators which contain finite sums of products of two Toeplitz operators with harmonic symbols. We give characterizations of when an operator in that class is zero or compact. Also, we solve the zero product problem for products of finitely many Toeplitz operators with harmonic symbols. 相似文献
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Young Joo Lee 《Journal of Mathematical Analysis and Applications》2007,329(2):1316-1329
We study some algebraic properties of Toeplitz operators on the Dirichlet space. We first characterize (semi-)commuting Toeplitz operators with harmonic symbols. Next we study the product problem of when product of two Toeplitz operators is another Toeplitz operator. As an application, we show that the zero product of two Toeplitz operators with harmonic symbol has only a trivial solution. Also, the corresponding compact product problem is studied. 相似文献
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Liankuo Zhao 《Journal of Mathematical Analysis and Applications》2008,339(2):1148-1160
In this paper, we completely characterize (semi-)commutativity of Toeplitz operators with harmonic symbols on harmonic Dirichlet space. 相似文献
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Yong Chen 《Journal of Mathematical Analysis and Applications》2009,357(1):214-224
In this paper, we study the commutativity of Toeplitz operators with continuous symbols on the Dirichlet space. First, under a mild condition concerning absolute continuity we characterize (semi-)commuting Toeplitz operators. This is a generalization of the case of harmonic symbols. Also, if one of the symbol is radial or analytic, we get another characterization, which is different from the case on the Bergman space. 相似文献
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Jianjun Chen Xiaofeng Wang Jin Xia Guangfu Cao 《Frontiers of Mathematics in China》2017,12(4):769-785
The present paper mainly gives some applications of Berezin type symbols on the Dirichlet space of unit ball. We study the solvability of some Riccati operator equations of the form XAX + XB - CX = D related to harmonic Toeplitz operators on the Dirichlet space. Especially, the invariant subspaces of Toeplitz operators are also considered. 相似文献