共查询到20条相似文献,搜索用时 265 毫秒
1.
Algebraic and spectral properties of dual Toeplitz operators 总被引:7,自引:0,他引:7
Karel Stroethoff Dechao Zheng 《Transactions of the American Mathematical Society》2002,354(6):2495-2520
Dual Toeplitz operators on the orthogonal complement of the Bergman space are defined to be multiplication operators followed by projection onto the orthogonal complement. In this paper we study algebraic and spectral properties of dual Toeplitz operators.
2.
Zhijian Wu 《Integral Equations and Operator Theory》1996,24(3):352-371
We study the commutator of the multiplication and harmonic Bergman projection, Hankel and Toeplitz operators on the harmonic Bergman spaces. The same type operators have been well studied on the analytic Bergman spaces. The main difficulty of this study is that the bounded harmonic function space is not an algebra! In this paper, we characterize theL
p boundedness and compactness of these operators with harmonic symbols. Results about operators in Schatten classes, the cut-off phenomenon and general symbols are also included.Partially supported by a grant from the Research Grants Committee of the University of Alabama. 相似文献
3.
Zhang K.Feng X.Dong J.G.Guan C.Yu Y. 《数学学报》2015,(1):125-130
Multiplication operator is an important class of operators in function space. We mainly research the properties of the multiplication operator on the weighted Bergman space of the unit ball. ©, 2015, Chinese Academy of Sciences. All right reserved. 相似文献
4.
This paper mainly concerns a tuple of multiplication operators
defined on the weighted and unweighted multi-variable Bergman
spaces, their joint reducing subspaces and the von Neumann algebra
generated by the orthogonal projections onto these subspaces. It is
found that the weights play an important role in the structures of
lattices of joint reducing subspaces and of associated von Neumann
algebras. Also, a class of special weights is taken into account.
Under a mild condition it is proved that if those multiplication
operators are defined by the same symbols, then the corresponding
von Neumann algebras are $*$-isomorphic to the one defined on the
unweighted Bergman space. 相似文献
5.
Răzvan Gelca 《Integral Equations and Operator Theory》1997,28(2):191-195
We prove Bergman space analogues of a conjecture of Douglas and Paulsen related to the classification of invariant subspaces for multiplication operators in several variables. 相似文献
6.
Sherwin Kouchekian 《Integral Equations and Operator Theory》2003,45(3):319-342
The unbounded Bergman operator, the operator of multiplication
by on an unbounded open subset of the plane, is considered. We give a complete
answer regarding the density problem of unbounded Bergman operators
in terms of its equivalence to the problem of bounded point evaluations for the
Bergman spaces. Using this equivalence and the notion of Wiener capacity, we
obtain simple geometric conditions that classify almost those open subsets of
the plane for which the corresponding Bergman operators are densely defined.
With the aid of an analytic approach, we are also able to give condition for a
large collection of open subsets of the plane for which all the positive integer
powers of the corresponding Bergman operators are densely defined.
Submitted: December 14, 2001? Revised: January 14, 2001. 相似文献
7.
Commutative algebras of Toeplitz operators acting on the Bergman space on the unit disk have been completely classified in terms of geometric properties of the symbol class. The question when two Toeplitz operators acting on the harmonic Bergman space commute is still open. In some papers, conditions on the symbols have been given in order to have commutativity of two Toeplitz operators. In this paper, we describe three different algebras of Toeplitz operators acting on the harmonic Bergman space: The C*-algebra generated by Toeplitz operators with radial symbols, in the elliptic case; the C*-algebra generated by Toeplitz operators with piecewise continuous symbols, in the parabolic and hyperbolic cases. We prove that the Calkin algebra of the first two algebras are commutative, like in the case of the Bergman space, while the last one is not. 相似文献
8.
《数学物理学报(B辑英文版)》2020,(1)
In this article, we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables. Surprisingly, the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same. Also, some interesting symmetry properties of complex symmetric Toeplitz operators are obtained. 相似文献
9.
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
10.
This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space only with bounded weighted symbols if and only if the composition symbol is a finite Blaschke product. 相似文献
11.
解析函数的Banach空间上之复合算子 总被引:2,自引:0,他引:2
本文研究了一类解析函数的Banach空间X上之复合算子,这类空间包含了Bloch空间,并且可看作Bergman空间L1a(D)中具有原子分解的解析函数的对偶空间.我们刻划了这类空间上紧复合算子及Fredholm复合算子的特征,此外,还研究了具有闭值域的复合算子. 相似文献
12.
We consider the boundedness of composition operators on the Bergman space,and shows that when it is induced by automorphism is always bounded.At first we got a change of variables formula,which is very important for the proof of the boundedness of composition operators,and then obtain an upper bound for the special operator norm on Bergman space. 相似文献
13.
14.
15.
Namita Das 《印度理论与应用数学杂志》2010,41(2):379-400
In this paper the concept of asymptotic Toeplitz and asymptotic Hankel operators on the Bergman space are introduced and properties of these classes of operators are studied. The importance of this notion is that it associates with a class of operators a Toeplitz operator and with a class of operators a Hankel operator where the original operators are not even Toeplitz or Hankel. Thus it is possible to assign a symbol to an operator that is not Toeplitz or Hankel and hence a symbol calculus is obtained. Further a relation between Toeplitz operators and little Hankel operators on the Bergman space is established in some asymptotic sense. 相似文献
16.
Ondrej Hutník 《Integral Equations and Operator Theory》2011,71(3):357-388
We study a parameterized family of Toeplitz-type operators with respect to specific wavelets whose Fourier transforms are
related to Laguerre polynomials. On the one hand, this choice of wavelets underlines the fact that these operators acting
on wavelet subspaces share many properties with the classical Toeplitz operators acting on the Bergman spaces. On the other
hand, it enables to study poly-Bergman spaces and Toeplitz operators acting on them from a different perspective. Restricting
to symbols depending only on vertical variable in the upper half-plane of the complex plane these operators are unitarily
equivalent to a multiplication operator with a certain function. Since this function is responsible for many interesting features
of these Toeplitz-type operators and their algebras, we investigate its behavior in more detail. As a by-product we obtain
an interesting observation about the asymptotic behavior of true poly-analytic Bergman spaces. Isomorphisms between the Calderón-Toeplitz
operator algebras and functional algebras are described and their consequences in time-frequency analysis and applications
are discussed. 相似文献
17.
Let p be an analytic polynomial on the unit disk. We obtain a necessary and sufficient condition for Toeplitz operators with the symbol z + p to be invertible on the Bergman space when all coefficients of p are real numbers. Furthermore, we establish several necessary and sufficient, easy-to-check conditions for Toeplitz operators with the symbol z + p to be invertible on the Bergman space when some coefficients of p are complex numbers. 相似文献
18.
Kehe Zhu 《Journal of Functional Analysis》2003,202(2):327-341
For a finite Blaschke product B let TB denote the analytic multiplication operator (also called a Toeplitz operator) on the Bergman space of the unit disk. We show that the defect operators and both map the Bergman space to the Hardy space and the Hardy space to the Dirichlet space. 相似文献
19.
本文讨论多复变Bergman空间上坐标乘子组联合酉等价的条件以及与多复变Hardy空间上Toeplitz算子组的关系 相似文献
20.
In this paper, we study the commutativity of Toeplitz operators with radial symbols on the pluriharmonic Bergman space. We obtain the necessary and sufficient conditions for the commutativity of bounded Toeplitz operator and Toeplitz operator with radial symbol on the pluriharmonic Bergman space. 相似文献