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1.
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
2.
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
3.
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
4.
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
5.
Hyoung Joon Kim 《Integral Equations and Operator Theory》2008,61(1):103-120
In this paper we consider the hyperinvariant subspace problem for quasinilpotent operators. Let denote the class of quasinilpotent quasiaffinities Q in such that Q
*
Q has an infinite dimensional reducing subspace M with Q
*
Q|
M
compact. It was known that if every quasinilpotent operator in has a nontrivial hyperinvariant subspace, then every quasinilpotent operator has a nontrivial hyperinvariant subspace. Thus
it suffices to solve the hyperinvariant subspace problem for elements in . The purpose of this paper is to provide sufficient conditions for elements in to have nontrivial hyperinvariant subspaces. We also introduce the notion of “stability” of extremal vectors to give partial
solutions to the hyperinvariant subspace problem.
相似文献
6.
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
7.
8.
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
9.
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
10.
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
11.
S. Shkarin 《Integral Equations and Operator Theory》2009,64(1):115-136
It is shown that if 1 < p < ∞ and X is a subspace or a quotient of an ℓp-direct sum of finite dimensional Banach spaces, then for any compact operator T on X such that ∥I + T∥ > 1, the operator I + T attains its norm. A reflexive Banach space X and a bounded rank one operator T on X are constructed such that ∥I + T∥ > 1 and I + T does not attain its norm.
The author would like to thank E. Shargorodsky for his interest and comments. 相似文献
12.
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
13.
Matthew Kennedy Victor S. Shulman Yuri V. Turovskii 《Integral Equations and Operator Theory》2009,63(1):47-93
We show that finitely subgraded Lie algebras of compact operators have invariant subspaces when conditions of quasinilpotence
are imposed on certain components of the subgrading. This allows us to obtain some useful information about the structure
of such algebras. As an application, we prove a number of results on the existence of invariant subspaces for algebraic structures
of compact operators, in particular for Jordan algebras and Lie triple systems of Volterra operators. Along the way we obtain
new criteria for the triangularizability of a Lie algebra of compact operators.
The support received from INTAS project No 06-1000017-8609 is gratefully acknowledged by the third author. 相似文献
14.
Pascal Lefèvre 《Integral Equations and Operator Theory》2009,63(4):557-569
We compute the essential norm of a composition operator relatively to the class of Dunford-Pettis operators or weakly compact
operators, on some uniform algebras of analytic functions. Even in the context of H∞ (resp. the disk algebra), this is new, as well for the polydisk algebras and the polyball algebras. This is a consequence
of a general study of weighted composition operators.
相似文献
15.
M. A. Nudelman 《Integral Equations and Operator Theory》2007,58(2):273-299
Let
I
m
is the identity matrix of order m. Let W(λ) be an entire matrix valued function of order 2m, W(0) = I
2m
, the values of W(λ) are j
mm
-unitary at the imaginary axis and strictly j
mm
-expansive in the open right half-plane. The blocks of order m of the matrix W(λ) with appropriate signs are treated as coefficients of algebraic Riccati equation. It is proved that for any λ with positive
real part this equation has a unique contractive solution θ(λ). The matrix valued function θ(λ) can be represented in a form θ(λ) = θ
A
(iλ) where θ
A
(μ) is the characteristic function of some maximal dissipative operator A. This operator is in a natural way constructed starting from the Hamiltonian system of the form
with periodic coefficients. 相似文献
16.
Tomas Ya. Azizov Jussi Behrndt Peter Jonas Carsten Trunk 《Integral Equations and Operator Theory》2009,63(2):151-163
For closed linear operators or relations A and B acting between Hilbert spaces and the concepts of compact and finite rank perturbations are defined with the help of the orthogonal projections P
A
and P
B
in onto the graphs of A and B. Various equivalent characterizations for such perturbations are proved and it is shown that these notions are a natural
generalization of the usual concepts of compact and finite rank perturbations.
Sadly, our colleague and friend Peter Jonas passed away on July, 18th 2007. 相似文献
17.
V. A. Khatskevich M. I. Ostrovskii V. S. Shulman 《Integral Equations and Operator Theory》2007,59(1):19-34
Properties of sets of solutions to inequalities of the form
are studied, where A, B, C are bounded Hilbert space operators, A and C are self-adjoint. Properties under consideration: closeness and interior points in standard operator topologies, convexity,
non-emptiness. 相似文献
18.
19.
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
20.
Fredholm criteria and index formulas are established for Wiener-Hopf operators W(a) with semi-almost periodic matrix symbols a on weighted Lebesgue spaces where 1 < p < ∞, w belongs to a subclass of Muckenhoupt weights and . We also study the invertibility of Wiener-Hopf operators with almost periodic matrix symbols on . In the case N = 1 we also obtain a semi-Fredholm criterion for Wiener-Hopf operators with semi-almost periodic symbols and, for another
subclass of weights, a Fredholm criterion for Wiener-Hopf operators with semi-periodic symbols.
Work was supported by the SEP-CONACYT Project No. 25564 (México). The second author was also sponsored by the CONACYT scholarship
No. 163480. 相似文献