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1.
The compact differences of composition operators acting on the weighted L 2-Bergman space over the unit disk is characterized by the angular derivative cancellation property and due to Moorhouse. In this paper we extend Moorhouse’s characterization, as well as some related results, to the ball and, at the same time, to the weighted L p -Bergman space for the full range of p. 相似文献
2.
Linear relations in the Calkin algebra for composition operators 总被引:1,自引:0,他引:1
Thomas Kriete Jennifer Moorhouse 《Transactions of the American Mathematical Society》2007,359(6):2915-2944
We consider this and related questions: When is a finite linear combination of composition operators, acting on the Hardy space or the standard weighted Bergman spaces on the unit disk, a compact operator?
3.
Boo Rim Choe Hyungwoon Koo Wayne Smith 《Transactions of the American Mathematical Society》2003,355(7):2829-2855
We study the action of composition operators on Sobolev spaces of analytic functions having fractional derivatives in some weighted Bergman space or Hardy space on the unit disk. Criteria for when such operators are bounded or compact are given. In particular, we find the precise range of orders of fractional derivatives for which all composition operators are bounded on such spaces. Sharp results about boundedness and compactness of a composition operator are also given when the inducing map is polygonal.
4.
Jennifer Moorhouse 《Journal of Functional Analysis》2005,219(1):70-92
A characterization of compact difference is given for composition operators acting on the standard weighted Bergman spaces and necessary conditions are given on a larger scale of weighted Dirichlet spaces. Conditions are given under which a composition operator can be written as a finite sum of composition operators modulo the compacts. The additive structure of the space of composition operators modulo the compact operators is investigated further and a sufficient condition is given to insure that two composition operators lie in the same component. 相似文献
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6.
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
7.
Fengying Li 《Integral Equations and Operator Theory》2013,75(4):517-525
In this paper, we show that on the weighted Bergman space of the unit disk the essential norm of a noncompact Hankel operator equals its distance to the set of compact Hankel operators and is realized by infinitely many compact Hankel operators, which is analogous to the theorem of Axler, Berg, Jewell and Shields on the Hardy space in Axler et al. (Ann Math 109:601–612, 1979); moreover, the distance is realized by infinitely many compact Hankel operators with symbols continuous on the closure of the unit disk and vanishing on the unit circle. 相似文献
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9.
Pekka J. Nieminen 《Journal of Mathematical Analysis and Applications》2011,382(2):565-576
We derive exact formulas for the essential and weak essential norms of weighted analytic composition operators acting on certain function spaces in the unit disc, extending and improving earlier results due to Sarason and to Kriete and Moorhouse. Differences of composition operators are also considered. The formulas involve the Aleksandrov measures associated to the symbol of the operator. The results are based on a variant of a general method due to Weis of constructing best compact and weakly compact approximants for linear operators on L1 spaces. 相似文献
10.
In the setting of the weighted Bergman space over the unit disk, we characterize Hilbert?CSchmidt differences of two composition operators in terms of integrability condition involving pseudohyperbolic distance between the inducing functions. We also show that a linear combination of two composition operators can be Hilbert?CSchmidt, except for trivial cases, only when it is essentially a difference. We apply our results to study the topological structure of the space of all composition operators under the Hilbert?CSchmidt norm topology. We first characterize components and then provide some sufficient conditions for isolation or for non-isolation. 相似文献
11.
Paul S. Bourdon 《Journal of Functional Analysis》2008,255(8):1995-2012
We give an elementary proof of a formula recently obtained by Hammond, Moorhouse, and Robbins for the adjoint of a rationally induced composition operator on the Hardy space H2 [Christopher Hammond, Jennifer Moorhouse, Marian E. Robbins, Adjoints of composition operators with rational symbol, J. Math. Anal. Appl. 341 (2008) 626-639]. We discuss some variants and implications of this formula, and use it to provide a sufficient condition for a rationally induced composition operator adjoint to be a compact perturbation of a weighted composition operator. 相似文献
12.
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
13.
设qo是单位多圆柱Dn到自身的—个全纯映射,ψ是Dn上的—个全纯函数.本文研究单位多圆柱上从Bergman空间Ap(Dn)到Bloch空间β(Dn)的加权复合算子Tψ,ψ通过全纯映射ψ和全纯函数ψ的函数特征。分别给出了单位多圆柱上从Bergman空间AP(Dn)到Bloch空间β(Dn)的加权复合算子Tψ,ψ有界性和紧性的充分必要条件. 相似文献
14.
We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed
with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we
find conditions to ensure that two weighted composition operators are in the same path connected component if the difference
of them is compact. Moreover, we compare the topologies induced by L(H∞) and L(H∞v) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated. 相似文献
15.
In this work we characterize the bounded and the compact weighted composition operators from the space $H^\infty $ of bounded analytic functions on the open unit disk into the Zygmund space and the little Zygmund space. We also provide boundedness and compactness criteria of the weighted composition operators from the Bloch space into the little Zygmund space. In particular, we show that the bounded operators between these spaces are necessarily compact. 相似文献
16.
Weighted composition operators have been related to products of composition operators and their adjoints and to isometries of Hardy spaces. In this paper, Hermitian weighted composition operators on weighted Hardy spaces of the unit disk are studied. In particular, necessary conditions are provided for a weighted composition operator to be Hermitian on such spaces. On weighted Hardy spaces for which the kernel functions are ${(1 - \overline{w}z)^{-\kappa}}$ for κ ≥ 1, including the standard weight Bergman spaces, the Hermitian weighted composition operators are explicitly identified and their spectra and spectral decompositions are described. Some of these Hermitian operators are part of a family of closely related normal weighted composition operators. In addition, as a consequence of the properties of weighted composition operators, we compute the extremal functions for the subspaces associated with the usual atomic inner functions for these weighted Bergman spaces and we also get explicit formulas for the projections of the kernel functions on these subspaces. 相似文献
17.
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
18.
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
19.
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
20.
Valentin Matache 《Complex Analysis and Operator Theory》2008,2(1):169-197
Operators on function spaces acting by composition to the right with a fixed selfmap φ of some set are called composition operators of symbol φ. A weighted composition operator is an operator equal to a composition operator followed by a multiplication operator. We
summarize the basic properties of bounded and compact weighted composition operators on the Hilbert Hardy space on the open
unit disk and use them to study composition operators on Hardy–Smirnov spaces.
Submitted: January 30, 2007. Revised: June 19, 2007. Accepted: July 11, 2007. 相似文献