共查询到20条相似文献,搜索用时 31 毫秒
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CAO Guangfu 《数学年刊B辑(英文版)》2002,23(3):385-396
The automorphism group of the Toeplitz C-algebra,J(C~1),generated by Toeplitz op-erators with C~1-symbols on Dirichlet space D is discussed;the K_0,X_1-groups and the firstcohomology group of J(C~1)are computed.In addition,the author provs that the spectraof Toeplitz operators with C~1-symbols are always connected,and discusses the algebraic prop-erties of Toeplitz operators.In particular,it is proved that there is no nontrivial selfadjointToeplitz operator on D and T_φ~*=T_φ if and only if T_φ is a scalar operator. 相似文献
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Kenneth R Davidson 《Journal of Functional Analysis》1977,24(3):291-302
We prove that an operator on H2 of the disc commutes modulo the compacts with all analytic Toeplitz operators if and only if it is a compact perturbation of a Toeplitz operator with symbol in H∞ + C. Consequently, the essential commutant of the whole Toeplitz algebra is the algebra of Toeplitz operators with symbol in QC. The image in the Calkin algebra of the Toeplitz operators with symbol in H∞ + C is a maximal abelian algebra. These results lead to a characterization of automorphisms of the algebra of compact perturbations of the analytic Toeplitz operators. 相似文献
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许庆祥 《中国科学A辑(英文版)》2002,45(4):462-469
Diagonal invariant ideals of Toeplitz algebras defined on discrete groups are introduced and studied. In terms of isometric
representations of Toeplitz algebras associated with quasi-ordered groups, a character of a discrete group to be amenable
is clarified. It is proved that whenG is Abelian, a closed twosided non-trivial ideal of the Toeplitz algebra defined on a discrete Abelian ordered group is diagonal
invariant if and only if it is invariant in the sense of Adji and Murphy, thus a new proof of their result is given. 相似文献
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We revisit the shift‐and‐invert Arnoldi method proposed in [S. Lee, H. Pang, and H. Sun. Shift‐invert Arnoldi approximation to the Toeplitz matrix exponential, SIAM J. Sci. Comput., 32: 774–792, 2010] for numerical approximation to the product of Toeplitz matrix exponential with a vector. In this approach, one has to solve two large‐scale Toeplitz linear systems in advance. However, if the desired accuracy is high, the cost will be prohibitive. Therefore, it is interesting to investigate how to solve the Toeplitz systems inexactly in this method. The contribution of this paper is in three regards. First, we give a new stability analysis on the Gohberg–Semencul formula (GSF) and define the GSF condition number of a Toeplitz matrix. It is shown that when the size of the Toeplitz matrix is large, our result is sharper than the one given in [M. Gutknecht and M. Hochbruck. The stability of inversion formulas for Toeplitz matrices, Linear Algebra Appl., 223/224: 307–324, 1995]. Second, we establish a relation between the error of Toeplitz systems and the residual of Toeplitz matrix exponential. We show that if the GSF condition number of the Toeplitz matrix is medium‐sized, then the Toeplitz systems can be solved in a low accuracy. Third, based on this relationship, we present a practical stopping criterion for relaxing the accuracy of the Toeplitz systems and propose an inexact shift‐and‐invert Arnoldi algorithm for the Toeplitz matrix exponential problem. Numerical experiments illustrate the numerical behavior of the new algorithm and show the effectiveness of our theoretical results. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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We show that every \(n\,\times \,n\) matrix is generically a product of \(\lfloor n/2 \rfloor + 1\) Toeplitz matrices and always a product of at most \(2n+5\) Toeplitz matrices. The same result holds true if the word ‘Toeplitz’ is replaced by ‘Hankel,’ and the generic bound \(\lfloor n/2 \rfloor + 1\) is sharp. We will see that these decompositions into Toeplitz or Hankel factors are unusual: We may not, in general, replace the subspace of Toeplitz or Hankel matrices by an arbitrary \((2n-1)\)-dimensional subspace of \({n\,\times \,n}\) matrices. Furthermore, such decompositions do not exist if we require the factors to be symmetric Toeplitz or persymmetric Hankel, even if we allow an infinite number of factors. 相似文献
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The conjugate-normal Toeplitz problem is the one of characterizing the matrices that are conjugate-normal and Toeplitz at the same time. Based on a result of Gu and Patton and our results related to the normal Hankel problem, we show that a complex matrix is conjugate-normal and Toeplitz if and only if it is in one of the seven classes explicitly described in our paper. 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 study positive Toeplitz operators on the harmonic Bergman space via their Berezin transforms. We consider the Toeplitz operators with continuous harmonic symbols on the closed disk and show that the Toeplitz operator is positive if and only if its Berezin transform is nonnegative on the disk. On the other hand, we construct a function such that the Toeplitz operator with this function as the symbol is not positive but its Berezin transform is positive on the disk. We also consider the harmonic Bergman space on the upper half plane and prove that in this case the positive Toeplitz operators with continuous integrable harmonic symbols must be the zero operator. 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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解析Toeplitz代数的本质换位及其相关问题 总被引:1,自引:1,他引:0
在本文中,我们决定出多复变Hardy空间H2上解析Toeplitz代数的本质换位.即一个算子与所有解析Toeplitz算子本质可换,当且仅当它是符号属于Ac的Toeplitz算子的紧扰动.由此,符号属于Ac的Toeplitz算子生成的代数F(Ac)在Calkin代数中的像是极大可换闭代数,这导致了L.Coburn正合列的极大扩充.从这个事实,证明了符号属于Ac的Toeplitz算子的本质谱是连通的,这大大改进了C-S最近的工作.从本文的主要定理,证明了Toeplitz代数F(L∞)的本质换位和本质中心是由符号属于QC的Toeplitz算子生成的代数F(QC),这些结果又导致了对代数F(H∞)+K自同构群的确定. 相似文献
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Akaki Tikaradze 《Complex Analysis and Operator Theory》2012,6(6):1275-1279
In this note we describe centralizers of Toeplitz operators with polynomial symbols on the Bergman space. As a consequence it is shown that if an element of the norm closed algebra generated by all Toeplitz operators commutes with a Toeplitz operator of a nonconstant polynomial, then this element is a Toeplitz operator of a holomorphic function. 相似文献
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In this paper we investigate some algebra properties of dual Toeplitz operators on the orthogonal complement of the Dirichlet space in the Sobolev space. We completely characterize commuting dual Toeplitz operators with harmonic symbols, and show that a dual Toeplitz operator commutes with a nonconstant analytic dual Toeplitz operator if and only if its symbol is analytic. We also obtain the sufficient and necessary conditions on the harmonic symbols for SφSφψ= Sφψ. 相似文献
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Dirichlet空间上Toeplitz算子的紧性 总被引:1,自引:0,他引:1
本文给出了 Dirichlet空间上 Toelpitz算子为紧算子的充要条件,并证明具有 C1-符号的 Toeplitz算子为紧算子当且仅当它为零算子,当且仅当符号的边值为零. 相似文献
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本文给出了Dirichlet空间上Toelpitz算子为紧算子的充要条件.并证明具有C 相似文献
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多连通域的Bergman空间上的Toeplitz算子 总被引:2,自引:0,他引:2
In this paper, we investigate the Toeplitz operators with positive measure symbols on the Bergman spaces of bounded multi-connected domains and show that a Toeplitz operator is bounded or compact if and only if the symbol measure is a Carleson or vanishing Carleson measure respectively. 相似文献