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1.
A. Böttcher S. Grudsky E. A. Maksimenko J. Unterberger 《Integral Equations and Operator Theory》2009,63(2):165-180
The paper is concerned with Hermitian Toeplitz matrices generated by a class of unbounded symbols that emerge in several applications.
The main result gives the third order asymptotics of the extreme eigenvalues and the first order asymptotics of the extreme
eigenvectors of the matrices as their dimension increases to infinity.
This work was partially supported by CONACYT projects 60160 and 80504, Mexico. 相似文献
2.
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
3.
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
4.
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
5.
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
6.
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
7.
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
8.
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
9.
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
10.
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
11.
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
12.
B. P. Duggal 《Integral Equations and Operator Theory》2009,63(1):17-28
A Banach space operator T ∈ B(χ) is polaroid if points λ ∈ iso σ(T) are poles of the resolvent of T. Let denote, respectively, the approximate point, the Weyl, the Weyl essential approximate, the upper semi–Fredholm and lower
semi–Fredholm spectrum of T. For A, B and C ∈ B(χ), let M
C
denote the operator matrix . If A is polaroid on , M
0 satisfies Weyl’s theorem, and A and B satisfy either of the hypotheses (i) A has SVEP at points and B has SVEP at points , or, (ii) both A and A* have SVEP at points , or, (iii) A* has SVEP at points and B
* has SVEP at points , then . Here the hypothesis that λ ∈ π0(M
C
) are poles of the resolvent of A can not be replaced by the hypothesis are poles of the resolvent of A.
For an operator , let . We prove that if A* and B* have SVEP, A is polaroid on π
a
0(M
C) and B is polaroid on π
a
0(B), then .
相似文献
13.
We define and study the Fock space associated with the spherical mean operator. Next, we establish some results for the Segal-Bergmann
transform for this space. Lastly, we prove some properties concerning Toeplitz operators on this space.
Received: May 11, 2007. Revised: May 20, 2008. Accepted: May 23, 2008. 相似文献
14.
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
15.
Yury M. Arlinskiĭ Seppo Hassi Henk S. V. de Snoo 《Complex Analysis and Operator Theory》2007,1(2):211-233
Passive linear systems τ =
have their transfer function
in the Schur class S
. Using a parametrization of contractive block operators the transfer function
is connected to the Sz.-Nagy–Foiaş characteristic function
of the contraction A. This gives a new aspect and some explicit formulas for studying the interplay between the system τ and the functions
and
. The method leads to some new results for linear passive discrete-time systems. Also new proofs for some known facts in
the theory of these systems are obtained.
Dedicated to Eduard Tsekanovskiĭ on the occasion of his seventieth birthday
This work was supported by the Research Institute for Technology at the University of Vaasa.
The first author was also supported by the Academy of Finland (projects 212146, 117617) and the Dutch Organization for Scientific
Research N.W.O. (B 61-553).
Received: December 22, 2006. Revised: February 6, 2007. 相似文献
16.
Isabelle Chalendar Antoine Flattot Nadine Guillotin-Plantard 《Archiv der Mathematik》2008,90(4):353-359
In this paper we study the point spectrum of the operator
where d ≥ 1, 1 ≤ p ≤ ∞([0, 1]
d
) and τ is an irrational rotation on [0, 1]
d
. For a particular class of weights w, the point spectrum of T
w,τ is shown to be empty, generalizing Davie’s result [3], who considered the case p = 2, d = 1.
Received: 1 June 2007, Revised: 16 October 2007 相似文献
17.
We revisit the boundedness of Hankel and Toeplitz operators acting on the Hardy space H
1 and give a new proof of the old result stating that the Hankel operator H
a
is bounded if and only if a has bounded logarithmic mean oscillation. We also establish a sufficient and necessary condition for H
a
to be compact on H
1. The Fredholm properties of Toeplitz operators on H
1 are studied for symbols in a Banach algebra similar to C + H
∞ under mild additional conditions caused by the differences in the boundedness of Toeplitz operators acting on H
1 and H
2.
The first author was partially supported by the European Commission IHP Network “Harmonic Analysis and Related Problems” (Contract
Number: HPRN-CT-2001-00273-HARP) and by the Greek Research Program “Pythagoras 2” (75% European funds and 25 National funds).
The second author was fully supported by the European Commission IHP Network “Harmonic Analysis and Related Problems” (Contract
Number: HPRN-CT-2001-00273-HARP) while he visited the first author at the University of Crete and later by the Academy of
Finland Project 207048. 相似文献
18.
Some properties and applications of meromorphic factorization of matrix functions are studied. It is shown that a meromorphic
factorization of a matrix function G allows one to characterize the kernel of the Toeplitz operator with symbol G without actually having to previously obtain a Wiener–Hopf factorization. A method to turn a meromorphic factorization into
a Wiener–Hopf one which avoids having to factorize a rational matrix that appears, in general, when each meromorphic factor
is treated separately, is also presented. The results are applied to some classes of matrix functions for which the existence
of a canonical factorization is studied and the factors of a Wiener–Hopf factorization are explicitly determined.
Submitted: April 15, 2007. Revised: October 26, 2007. Accepted: December 12, 2007. 相似文献
19.
Let be a multiplicative semigroup of positive operators on a Banach lattice E such that every is ideal-triangularizable, i.e., there is a maximal chain of closed subspaces of E that consists of closed ideals invariant under S. We consider the question under which conditions the whole semigroup is simultaneously ideal-triangularizable. In particular, we extend a recent result of G. MacDonald and H. Radjavi. We also
introduce a class of positive operators that contains all positive abstract integral operators when E is Dedekind complete.
相似文献
20.
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