共查询到20条相似文献,搜索用时 11 毫秒
1.
Donald Sarason 《Integral Equations and Operator Theory》2008,61(2):281-298
This partly expository article develops the basic theory of unbounded Toeplitz operators on the Hardy space H
2, with emphasis on operators whose symbols are not square integrable. Unbounded truncated Toeplitz operators on coinvariant
subspaces of H
2 are also studied.
In memory of Paul R. Halmos 相似文献
2.
On the setting of the half-space we introduce the Schatten-Herz classes of Toeplitz operators and obtain characterizations
for positive Toeplitz operators to belong to those classes. We also prove results concerning the boundedness and compactness
of Toeplitz operators with Herz symbols. Such a study has been recently done on the ball. At a critical step of the proofs
we employ a much simplified argument to extend the range of parameters for Herz spaces on which the Berezin transform is bounded.
Our results show not only that most of results on the ball continue to hold, but also that there is some pathology caused
by the unboundedness of the domain.
The first author was in part supported by a Korea University Grant(2007), the second author was in part supported by Hanshin
University Research Grant, and both authors were in part supported by KOSEF(R01-2003-000-10243-0). 相似文献
3.
Roberto C. Raimondo 《Integral Equations and Operator Theory》2007,57(3):425-449
In this paper we study the problem of the membership of H
ϕ in the Hilbert-Schmidt class, when
and Ω is a planar domain. We find a necessary and sufficient condition.We apply this result to the problem of joint membership
of H
φ and
in the Hilbert-Schmidt class. Using the notion of Berezin Transform and a result of K. Zhu we are able to give a necessary
and sufficient condition. Finally, we recover a result of Arazy, Fisher and Peetre on the case
with φ holomorphic. 相似文献
4.
An operatorX:
is said to be a generalized Toeplitz operator with respect to given contractionsT
1 andT
2 ifX=T
2XT1
*. The purpose of this line of research, started by Douglas, Sz.-Nagy and Foia, and Pták and Vrbová, is to study which properties of classical Toeplitz operators depend on their characteristic relation. Following this spirit, we give appropriate extensions of a number of results about Toeplitz operators. Namely, Wintner's theorem of invertibility of analytic Toeplitz operators, Widom and Devinatz's invertibility criteria for Toeplitz operators with unitary symbols, Hartman and Wintner's theorem about Toeplitz operator having a Fredholm symbol, Hartman and Wintner's estimate of the norm of a compactly perturbed Toeplitz operator, and the non-existence of compact classical Toeplitz operators due to Brown and Halmos.Dedicated to our friend Cora Sadosky on the occasion of her sixtieth birthday 相似文献
5.
In this paper we discuss an unusual phenomenon in the context of Toeplitz operators in the Bergman space on the unit disc:
If two Toeplitz operators commute with a quasihomogeneous Toeplitz operator, then they commute with each other. In the Bourbaki
terminology, this result can be stated as follows: The commutant of a quasihomogeneous Toeplitz operator is equal to its bicommutant.
Received: 11 March 2008 相似文献
6.
It is well known that there are classes of test functions such that a Hankel operator is bounded if and only if it is bounded
on those functions. Criteria are derived which determine whether a Hankel operator is compact or belongs to a particular Schatten
class, in terms of its action on those test functions. 相似文献
7.
Roberto C. Raimondo 《Integral Equations and Operator Theory》2008,62(2):219-232
In this paper we study the problem of the joint membership of Hφ and in the Schatten-von Neumann p-class when φ ∈ L∞(Ω) and Ω is a planar domain. We use a result of K. Zhu and the localization near the boundary to solve the problem. Finally,
we recover a result of Arazy, Fisher and Peetre on the case with φ holomorphic.
相似文献
8.
Jie Miao 《Integral Equations and Operator Theory》2007,59(1):53-65
We give a necessary and sufficient condition for Hankel operators Hf on the harmonic Bergman space of the unit ball to be in the Schatten p-class for 2 ≤ p < ∞. A special case when symbol f is a harmonic function is also considered. 相似文献
9.
Algebraic Properties of Toeplitz Operators with Radial Symbols on the Bergman Space of the Unit Ball
In this paper, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Bergman space of the
unit ball in . We first determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator. Next, we investigate
the zero-product problem for several Toeplitz operators with radial symbols. Also, the corresponding commuting problem of
Toeplitz operators whose symbols are of the form is studied, where and φ is a radial function.
Ze-Hua Zhou: supported in part by the National Natural Science Foundation of China (Grand Nos.10671141, 10371091). 相似文献
10.
Kyunguk Na 《Integral Equations and Operator Theory》2009,64(3):409-428
We study characterizations of arbitrary positive Toeplitz operators of Schatten (or Schatten-Herz) type in terms of averaging
functions and Berezin transforms of symbol functions on the ball of pluriharmonic Bergman space.
This work was supported by a Hanshin University Research Grant. 相似文献
11.
12.
We discuss the optimality of a sufficient condition from [12] for a point to belong to the essential spectrum of a Toeplitz
operator with a bounded measurable coefficient. Our approach is based on a new sufficient condition for a composition of a
Muckenhoupt weight with a Blaschke product to belong to the same Muckenhoupt class.
The first author was partially supported by CONACYT project U46936-F, Mexico. 相似文献
13.
Eugene Shargorodsky 《Integral Equations and Operator Theory》2007,57(1):127-132
We establish a sufficient condition for a point to belong to the essential spectrum of a Toeplitz operator with a bounded
measurable coefficient. This condition uses geometric information on the cluster values of the coefficient. 相似文献
14.
Suppose that is a trigonometric polynomial of the form (z) = Nn=-N an zn. It is well-known that T is normal if and only if | a– N| = | aN| and the Fourier coefficients of satisfy the following symmetry condition:
In this paper we provide a complete criterion for hyponormality of T when satisfies a partial symmetry condition:
相似文献
15.
Boo Rim Choe Hyungwoon Koo Michael Stessin 《Integral Equations and Operator Theory》2009,63(4):501-520
We obtain new characterizations of Carleson measures via uniform boundedness of BMO norms of certain mass functions associated
with the given measure in a natural way.
This research was performed during M. Stessin’s visit to Korea University. He thanks the Mathematics Department of Korea University
and the “Brain Pool” program for their hospitality and support. The first two authors were supported by the Korea Research
Foundation Grant funded by the Korean Government (KRF-2008-314-C00012). 相似文献
16.
Konstantin M. Dyakonov 《Mathematische Annalen》2009,344(2):353-380
For a Toeplitz operator T
φ
, we study the interrelationship between smoothness properties of the symbol φ and those of the functions annihilated by T
φ
. For instance, it follows from our results that if φ is a unimodular function on the circle lying in some Lipschitz or Zygmund space Λα with 0 < α < ∞, and if f is an H
p
-function (p ≥ 1) with T
φ
f = 0, then f ∈ Λα and
for some c = c(α, p) and d = d(α, p); an explicit formula for the optimal exponent d is provided. Similar—and more general—results for various smoothness classes are obtained, and several approaches are discussed.
Furthermore, since a given non-null function f ∈ H
p
lies in the kernel of with , we derive information on the smoothness of H
p
-functions with smooth arguments. This can be viewed as a natural counterpart to the existing theory of analytic functions
with smooth moduli.
Supported in part by grants MTM2008-05561-C02-01/MTM, HF2006-0211 and MTM2007-30904-E from El Ministerio de Ciencia e Innovación
(Spain), and by grant 2005-SGR-00611 from DURSI (Generalitat de Catalunya). 相似文献
17.
Benoit Florent Sehba 《Integral Equations and Operator Theory》2008,62(2):233-245
We present here some criteria for Schatten-Von Neumann class membership for the small Hankel operator on Bergman space A
2(T
Ω), when T
Ω is the tube over the symmetric cone Ω.
The author would like to thank professor Aline Bonami for helpful advices. 相似文献
18.
We study the problem of factorisation of non-negative Fredholm operators acting in the Hilbert space L2(0, 1) and its relation to the inverse spectral problem for Bessel operators. In particular, we derive an algorithm of reconstructing
the singular potential of the Bessel operator from its spectrum and the sequence of norming constants. 相似文献
19.
Constantin Buşe Mihail Megan Manuela-Suzy Prajea Petre Preda 《Integral Equations and Operator Theory》2007,59(4):491-500
Among others we shall prove that an exponentially bounded evolution family U = {U(t, s)}
t≥s≥0 of bounded linear operators acting on a Banach space X is uniformly exponentially stable if and only if there exists q
[1, ∞) such that
This result seems to be new even in the finite dimensional case and it is the strong variant of an old result of E. A. Barbashin
([1]Theorem 5.1).
The first author was partially supported by the CNCSIS’s grant no. 546/2006. 相似文献
20.
For a bounded function defined on
, let
be the set of singular values of the (n + 1) x (n + 1) matrix whose (j, k)-entries
are equal to
These matrices can be thought of as variable-coefficient Toeplitz matrices or
generalized Toeplitz matrices. Matrices of the above form can be also thought
of as the discrete analogue of pseudodifferential operators. Under a certain
smoothness assumption on the function , we prove that
where the constant c1 and a part of c2 are shown to have explicit integral
representations. The other part of c2 turns out to have a resemblance to the
Toeplitz case. This asymptotic formula can be viewed as a generalization of
the classical theory on singular values of Toeplitz matrices. 相似文献