共查询到20条相似文献,搜索用时 15 毫秒
1.
This paper studies algebras of functions on the unit disk generated byH
∞(D) and bounded harmonic functions. Using these algebras, we characterize compact semicommutators and commutators of Toeplitz
operators with harmonic symbols on the Bergman space.
Supported in part by the National Science Foundation and the University Research Council of Vanderbilt University. 相似文献
2.
Jie Miao 《Integral Equations and Operator Theory》1997,27(4):426-438
We study Toeplitz operators on the harmonic Bergman spaceb
p
(B), whereB is the open unit ball inR
n(n2), for 1<p. We give characterizations for the Toeplitz operators with positive symbols to be bounded, compact, and in Schatten classes. We also obtain a compactness criteria for the Toeplitz operators with continuous symbols. 相似文献
3.
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
4.
Alexander E. Richman 《Integral Equations and Operator Theory》2003,45(1):105-124
Following the work of C. Cowen and T. Kriete on the Hardy space, we prove that under a regularity condition, all composition
operators with a subnormal adjoint on A2(D) have linear fractional symbols of the form. Moreover, we show that all composition operators on the Bergman space having
these symbols have a subnormal adjoint, with larger range for the parameterr than found in the Hardy space case. 相似文献
5.
Hansong Huang 《Integral Equations and Operator Theory》2009,64(3):381-398
This paper mainly concerns abelian von Neumann algebras generated by Toeplitz operators on weighted Bergman spaces. Recently
a family of abelian w*-closed Toeplitz algebras has been obtained (see [5,6,7,8]). We show that this algebra is maximal abelian and is singly generated
by a Toeplitz operator with a “common” symbol. A characterization for Toeplitz operators with radial symbols is obtained and
generalized to the high dimensional case. We give several examples for abelian von Neumann algebras in the case of high dimensional
weighted Bergman spaces, which are different from the one dimensional case. 相似文献
6.
On the Bergman space of the unit ball in Cn, we solve the zero-product problem for two Toeplitz operators with harmonic symbols that have continuous extensions to (some part of) the boundary. In the case where symbols have Lipschitz continuous extensions to the boundary, we solve the zero-product problem for multiple products with the number of factors depending on the dimension n of the underlying space; the number of factors is n+3. We also prove a local version of this result but with loss of a factor. 相似文献
7.
We study the commuting problem for Toeplitz operators on the harmonic Bergman space of the unit disk. We show that an analytic Toeplitz operator and a co-analytic Toeplitz operator with certain noncyclicity hypothesis can commute only when one of their symbols is constant. We also obtain analogous results for semi-commutants. 相似文献
8.
Stephen M. Buckley M. S. Ramanujan Dragan Vukotić 《Integral Equations and Operator Theory》1999,35(1):1-19
This paper studies the boundedness and compactness of the coefficient multiplier operators between various Bergman spacesA
p
and Hardy spacesH
q
. Some new characterizations of the multipliers between the spaces with exponents 1 or 2 are derived which, in particular, imply a Bergman space analogue of the Paley-Rudin Theorem on sparse sequences. Hardy and Bergman spaces are shown to be linked using mixed-norm spaces, and this linkage is used to improve a known result on (A
p
,A
2), 1<p<2.Compact (H
1,H
2) and (A
1,A
2) multipliers are characterized. The essential norms and spectra of some multiplier operators are computed. It is shown that forp>1 there exist bounded non-compact multiplier operators fromA
p
toA
q
if and only ifpq. 相似文献
9.
Patrik Wahlberg 《Integral Equations and Operator Theory》2007,59(1):99-128
We study the short-time Fourier transformation, modulation spaces, Gabor representations and time-frequency localization operators,
for functions and tempered distributions that have as range space a Banach or a Hilbert space. In the Banach space case the
theory of modulation spaces contains some modifications of the scalar-valued theory, depending on the Banach space. In the
Hilbert space case the modulation spaces have properties similar to the scalar-valued case and the Gabor frame theory essentially
works. For localization operators in this context symbols are operator-valued. We generalize two results from the scalar-valued
theory on continuity on certain modulation spaces when the symbol belongs to an Lp,q space and M∞, respectively. The first result is true for any Banach space as range space, and the second result is true for any Hilbert
space as range space. 相似文献
10.
Compact Hankel operators on harmonic Bergman spaces 总被引:2,自引:0,他引:2
Mirjana Jovović 《Integral Equations and Operator Theory》1995,22(3):295-304
We study Hankel operators on the harmonic Bergman spaceb
2(B), whereB is the open unit ball inR
n,n2. We show that iff is in
then the Hankel operator with symbolf is compact. For the proof we have to extend the definition of Hankel operators to the spacesb
p(B), 1<p<, and use an interpolation theorem. We also use the explicit formula for the orthogonal projection ofL
2(B, dV) ontob
2(B). This result implies that the commutator and semi-commutator of Toeplitz operators with symbols in
are compact. 相似文献
11.
Peter R. Mercer 《Integral Equations and Operator Theory》1998,31(4):482-488
It is shown that a compact composition operator on a weighted Bergman space over a smoothly bounded strongly convex domain in
n
can have no angular derivative. Also, sufficient conditions for the boundedness and the compactness of composition operators defined on Hardy and weighted Bergman spaces are obtained, for situations in which each of the target spaces is enlarged in a natural way. 相似文献
12.
Products of Toeplitz Operators on the Bergman Space 总被引:1,自引:0,他引:1
Issam Louhichi Elizabeth Strouse Lova Zakariasy 《Integral Equations and Operator Theory》2006,54(4):525-539
In 1962 Brown and Halmos gave simple conditions for the product of two Toeplitz operators on Hardy space to be equal to a
Toeplitz operator. Recently, Ahern and Cucković showed that a similar result holds for Toeplitz operators with bounded harmonic
symbols on Bergman space. For general symbols, the situation is much more complicated. We give necessary and sufficient conditions
for the product to be a Toeplitz operator (Theorem 6.1), an explicit formula for the symbol of the product in certain cases
(Theorem 6.4), and then show that almost anything can happen (Theorem 6.7). 相似文献
13.
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
14.
Extending known results for the unit disk, we prove that for the unit ball there exist n+2 different cases of commutative C*-algebras generated by Toeplitz operators, acting on weighted Bergman spaces. In all cases the bounded measurable symbols
of Toeplitz operators are invariant under the action of certain commutative subgroups of biholomorphisms of the unit ball.
This work was partially supported by CONACYT Projects 46936 and 44620, México. 相似文献
15.
We analyze the influence of the radial component of a symbol to spectral, compactness, and Fredholm properties of Toeplitz operators, acting on the Bergman space. We show that there existcompact Toeplitz operators whose (radial) symbols areunbounded near the unit circle
. Studying this question we give several sufficient, and necessary conditions, as well as the corresponding examples. The essential spectra of Toeplitz operators with pure radial symbols have sufficiently rich structure, and even can be massive.TheC
*-algebras generated by Toeplitz operators with radial symbols are commutative, but the semicommutators[T
a, Tb)=Ta·Tb–Ta·b are not compact in general. Moreover for bounded operatorsT
a andT
b the operatorT
a·b may not be bounded at all.This work was partially supported by CONACYT Project 27934-E, México.The first author acknowledges the RFFI Grant 98-01-01023, Russia. 相似文献
16.
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
17.
Generalized Anti-Wick operators are introduced as a class of
pseudodifferential operators which depend on a symbol and two different window
functions. Using symbols in Sobolev spaces with negative smoothness and
windows in so-called modulation spaces, we derive new conditions for the
boundedness on L2 of such operators and for their membership in the Schatten
classes. These results extend and refine results contained in [20], [10], [5],
[4], and [14]. 相似文献
18.
19.
Antti Perälä 《Integral Equations and Operator Theory》2011,71(1):113-128
We study Toeplitz operators between analytic Bloch-type spaces of the unit disk. We construct suitable classes of distributions
that generate bounded Toeplitz operators between these spaces. The classes are naturally connected to the corresponding results
in the reflexive Bergman space setting and previously known results on A
1 and the Bloch space. We also study distributional symbols satisfying logarithmic BMO-condition. In addition, sufficient compactness
criteria are provided. 相似文献
20.
On the Bergman space of the unit polydisk in the complex n-space, we solve the zero-product problem for two Toeplitz operators with n-harmonic symbols that have local continuous extension property up to the distinguished boundary. In the case where symbols
have additional Lipschitz continuity up to the whole distinguished boundary, we solve the zero-product problem for products
with four factors. We also prove a local version of this result for products with three factors. 相似文献