共查询到20条相似文献,搜索用时 31 毫秒
1.
Zen Harper 《Journal of Evolution Equations》2005,5(3):387-405
We study convolution operators on weighted Lebesgue spaces and obtain weight characterisations for boundedness of these operators
with certain kernels. Our main result is Theorem 3 which enables us to obtain results for certain kernel functions supported
on bounded intervals; in particular we get a direct proof of the known characterisations for Steklov operators in Section
3 by using the weighted Hardy inequality. Our methods also enable us to obtain new results for other kernel functions in Section
4. In Section 5 we demonstrate that these convolution operators are related to operators arising from the Weiss Conjecture
(for scalar-valued observation functionals) in linear systems theory, so that results on convolution operators provide elementary examples of nearly bounded semigroups
not satisfying the Weiss Conjecture. Also we apply results on the Weiss Conjecture for contraction semigroups to obtain boundedness
results for certain convolution operators. 相似文献
2.
Andrew Wynn 《Complex Analysis and Operator Theory》2010,4(1):109-131
In this paper a weighted form of the Weiss conjecture is studied. For certain weights, the conjecture is shown to hold for
normal contraction operators related to discrete time linear systems. This is proved by an application of the Carleson measure
theorem for weighted Dirichlet spaces. The result for discrete time systems is used to show that a weighted form of the Weiss
conjecture holds for normal operators generating bounded C0-semigroups. Previously, weighted admissibility has been characterised for generators of analytic semigroups. No such assumption
of analyticity is made here. Additionally, results are presented regarding weighted Carleson measures, fractional powers of
normal operators and weighted composition operators. 相似文献
3.
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
4.
The gap between hyponormal and subnormal Hilbert space operators can be studied using the intermediate classes of weakly n-hyponormal and (strongly) n-hyponormal operators. The main examples for these various classes, particularly to distinguish them, have been the weighted
shifts. In this paper we first obtain a characterization for a weakly n-hyponormal weighted shift Wα with weight sequence α, from which we extend some known results for quadratically hyponormal (i.e., weakly 2-hyponormal)
weighted shifts to weakly n-hyponormal weighted shifts. In addition, we discuss some new examples for weakly n-hyponormal weighted shifts; one illustrates the differences among the classes of 2-hyponormal, quadratically hyponormal,
and positively quadratically hyponormal operators. 相似文献
5.
The Weiss conjecture on admissibility of observation operators for contraction semigroups 总被引:4,自引:0,他引:4
We prove the conjecture of George Weiss for contraction semigroups on Hilbert spaces, giving a characterization of infinite-time admissible observation functionals for a contraction semigroup, namely that such a functionalC is infinite-time admissible if and only if there is anM>0 such that
for alls in the open right half-plane. HereA denotes the infinitesimal generator of the semigroup. The result provides a simultaneous generalization of several celebrated results from the theory of Hardy spaces involving Carleson measures and Hankel operators. 相似文献
6.
Takuya Hosokawa Keiji Izuchi Shûichi Ohno 《Integral Equations and Operator Theory》2005,53(4):509-526
We study properties of the topological space of weighted composition operators on the space of bounded analytic functions
on the open unit disk in the uniform operator topology. Moreover, we characterize the compactness of differences of two weighted
composition operators. 相似文献
7.
In this paper, we study the weighted compositon operators on weighted Bergman spaces of bounded symmetric domains. The necessary
and sufficient conditions for a weighted composition operator W
φψ to be bounded and compact are studied by using the Carleson measure techniques. In the last section, we study the Schatten
p-class weighted composition operators. 相似文献
8.
Stevo Stevi? 《Applied mathematics and computation》2010,217(5):1811-6197
We find an asymptotically equivalent expression to the essential norm of differences of weighted composition operators between weighted-type spaces of holomorphic functions on the unit ball in CN. As a consequence we characterize the compactness of these operators. The boundedness of these operators is also characterized. 相似文献
9.
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
10.
加权Bergman空间上的Carleson测度与复合算子 总被引:2,自引:0,他引:2
本文研究了复平面上单位圆盘D上具有指数型权的加权Bergman空间上的Carleson测度和复合算子。利用Carleson测度的概念分别给出了有界或紧的复合算子的充分必要条件。 相似文献
11.
The Iterated Aluthge Transform of an Operator 总被引:1,自引:0,他引:1
The Aluthge transform (defined below) of an operator T on
Hilbert space has been studied extensively, most often in connection with
p-hyponormal operators. In [6] the present authors initiated a study of various
relations between an arbitrary operator T and its associated , and this
study was continued in [7], in which relations between the spectral pictures
of T and were obtained. This article is a continuation of [6] and [7]. Here
we pursue the study of the sequence of Aluthge iterates {
(n)} associated
with an arbitrary operator T. In particular, we verify that in certain cases
the sequence {
(n)} converges to a normal operator, which partially answers
Conjecture 1.11 in [6] and its modified version below (Conjecture 5.6).
Submitted: December 5, 2000? Revised: August 30, 2001. 相似文献
12.
In this paper we consider a class of weighted integral operators onL
2 (0, ) and show that they are unitarily equivalent to Hankel operators on weighted Bergman spaces of the right half plane. We discuss conditions for the Hankel integral operator to be finite rank, Hilbert-Schmidt, nuclear and compact, expressed in terms of the kernel of the integral operator. For a particular class of weights these operators are shown to be unitarily equivalent to little Hankel operators on weighted Bergman spaces of the disc, and the symbol correspondence is given. Finally the special case of the unweighted Bergman space is considered and for this case, motivated by approximation problems in systems theory, some asymptotic results on the singular values of Hankel integral operators are provided. 相似文献
13.
Zenon J. Jaboski 《Integral Equations and Operator Theory》2002,44(3):316-336
Athavale introduced in [3] the notion of a completely hyperexpansive operator. In this paper some results concerning powers of completely (alternatingly) hyperexpansive operators (not necessarily bounded) are extended tok-hyperexpansive ones. A semispectral measure is associated with a subnormal contraction as well as with a completely hyperexpansive operator, and an operator version of the Levy-Khinchin representation is obtained. Passing to the Naimark dilation of the semispectral measure, such an operator is related to a positive contraction in a natural way. New characterizations of a completely hyperexpansive operator and a subnormal contraction are given. The power bounded completely hyperexpansive operators are characterized. All these are illustrated using weighted shifts. 相似文献
14.
Cn中有界对称域上不同加权Dirichlet空间之间的复合算子 总被引:2,自引:0,他引:2
§1. IntroductionLetΩbeaboundedsymmetricdomainwithitsstandardrealizationinCnandnormalized(Euclidean)volumemeasuresothatυ(Ω)=1.LetK(·,z)denotetheBergmankernalfunc-tionatz∈Ω.TheBergmanmetriconΩisdefinedbyGz=(gij(z))=122zizjlogK(z,z) 1i,jn.Ifγ:[0,1]… 相似文献
15.
We prove that Jacobi, CMV, and Schrödinger operators, which are reflectionless on a homogeneous set E (in the sense of Carleson), under the assumption of a Blaschke-type condition on their discrete spectra accumulating at E, have purely absolutely continuous spectrum on E. 相似文献
16.
We study differences of weighted composition operators between weighted Banach spaces H
ν
∞ of analytic functions with weighted sup-norms and give an expression for the essential norm of these differences. We apply
our result to estimate the essential norm of differences of composition operators acting on Bloch-type spaces.
Authors’ addresses: Mikael Lindstr?m, Department of Mathematics, Abo Akademi University, FIN 20500 Abo, Finland; Elke Wolf,
Mathematical Institute, University of Paderborn, D-33095 Paderborn, Germany 相似文献
17.
Differences of Composition Operators between Weighted Banach Spaces of Holomorphic Functions on the Unit Polydisk 总被引:1,自引:0,他引:1
Elke Wolf 《Results in Mathematics》2008,51(3-4):361-372
We consider differences of composition operators between given weighted Banach spaces H
∞
v
or H
0
v
of analytic functions defined on the unit polydisk D
N
with weighted sup-norms and give estimates for the distance of these differences to the space of compact operators. We also
study boundedness and compactness of the operators. This paper is an extension of [6] where the one-dimensional case is treated.
Received: May 15, 2007. Revised: October 8, 2007. 相似文献
18.
Hardy空间之间的加权复合算子 总被引:7,自引:0,他引:7
本文研究了复平面中单位圆盘D上不同Hardy空间之间的加权复合算子,利用Carleson测度的概念分别给出了有界或紧的加权复合算子的充分必要条件。本文也用角数的概念给出了紧加权复合算子的一个必要条件。 相似文献
19.
James E. Jamison 《Integral Equations and Operator Theory》2006,56(4):469-482
A pair of operators on a Banach space X are isometrically equivalent if they are intertwined by a surjective isometry of X. We investigate the isometric equivalence problem for pairs of operators on specific types of Banach spaces. We study weighted
shifts on symmetric sequence spaces, elementary operators acting on an ideal I of Hilbert space operators, and composition operators on the Bloch space. This last case requires an extension of known results
about surjective isometries of the Bloch space. 相似文献
20.
In this paper, we study two-weight norm inequalities for operators of potential type in homogeneous spaces. We improve some of the results given in [6] and [8] by significantly weakening their hypotheses and by enlarging the class of operators to which they apply. We also show that corresponding results of Carleson type for upper half-spaces can be derived as corollaries of those for homogeneous spaces. As an application, we obtain some necessary and sufficient conditions for a large class of weighted norm inequalities for maximal functions under various assumptions on the measures or spaces involved.Research of the first author was supported in part by NSERC grant A5149.Research of the second author was supported in part by NSF grant DMS93-02991. 相似文献