共查询到20条相似文献,搜索用时 328 毫秒
1.
Young Joo Lee 《Journal of Mathematical Analysis and Applications》2007,329(2):1316-1329
We study some algebraic properties of Toeplitz operators on the Dirichlet space. We first characterize (semi-)commuting Toeplitz operators with harmonic symbols. Next we study the product problem of when product of two Toeplitz operators is another Toeplitz operator. As an application, we show that the zero product of two Toeplitz operators with harmonic symbol has only a trivial solution. Also, the corresponding compact product problem is studied. 相似文献
2.
Yong Chen Young Joo Lee Quang Dieu Nguyen 《Integral Equations and Operator Theory》2011,69(2):183-201
We study some algebraic properties of Toeplitz operators on the harmonic Dirichlet space of the unit disk. We first give a
characterization for boundedness of Toeplitz operators. Next we characterize commuting Toeplitz operators. Also, we study
the product problem of when product of two Toeplitz operators is another Toeplitz operator. The corresponding problems for
compactness are also studied. 相似文献
3.
4.
Young Joo Lee 《Journal of Mathematical Analysis and Applications》2009,357(2):504-515
On the Dirichlet space of the unit disk, we consider a class of operators which contain finite sums of products of two Toeplitz operators with harmonic symbols. We give characterizations of when an operator in that class is zero or compact. Also, we solve the zero product problem for products of finitely many Toeplitz operators with harmonic symbols. 相似文献
5.
In this paper, we study some algebraic properties of Toeplitz operators with quasihomogeneous symbols on the Dirichlet space of the unit ball Bn. First, we describe commutators of a radial Toeplitz operator and characterize commuting Toeplitz operators with quasihomogeneous symbols. Then we show that finite raak product of such operators only happens in the trivial case. Finally, some necessary and sufficient conditions are given for the product of two quasihomogeneous Toeplitz operators to be a quasihomogeneous Toeplitz operator. 相似文献
6.
7.
Matthias Lesch 《Integral Equations and Operator Theory》1991,14(1):120-145
In this paper we compute theK-groups of theC
*-algebra of Toeplitz operators on the Lie spheres. As a corollary we get an index theorem for Toeplitz operators with matricial symbols analogous to the index theorem of Berger, Coburn and Koranyi for Toeplitz operators with scalar valued symbols. 相似文献
8.
Xuanhao Ding 《Journal of Mathematical Analysis and Applications》2006,320(1):464-481
A limit theorem is established for a finite sum of finite products of Toeplitz operators on the Hardy space of the polydisk. As a consequence we show that the product of six Toeplitz operators with pluriharmonic symbols is compact iff the product equals zero iff one of these Toeplitz operators equals zero. 相似文献
9.
研究多重调和Bergman空间上的Topelitz算子.对多重调和符号的Topelitz算子,给出了乘积性质、交换性质的符号描述. 相似文献
10.
Xuanhao Ding 《Journal of Mathematical Analysis and Applications》2008,337(1):726-738
In this paper we completely characterize when the product of a Hankel operator and a Toeplitz operator on the Hardy space is a finite rank perturbation of a Hankel operator, and when the commutator of a Hankel operator and a Toeplitz operators has finite rank. 相似文献
11.
Lian Kuo Zhao 《数学学报(英文版)》2012,28(5):1033-1040
In this paper, we study Toeplitz operators with harmonic symbols on the harmonic Dirichlet space, and show that the product
of two Toeplitz operators is another Toeplitz operator only if one factor is constant. 相似文献
12.
Tao Yu 《Integral Equations and Operator Theory》2010,67(2):163-170
In this paper a decomposition of Sobolev space is obtained. Then we prove that a Toeplitz operator on the Dirichlet space
is compact only when it is the zero operator. For two Toeplitz operators on the Dirichlet space, we obtain the conditions
for that they commute, their product is a Toeplitz operator, and their commutator or semi-commutator has finite rank, respectively. 相似文献
13.
The paper is devoted to the study of specific properties of Toeplitz operators with (unbounded, in general) radial symbolsa=a(r). Boundedness and compactness conditions, as well as examples, are given. It turns out that there exist non-zero symbols which generate zero Toeplitz operators. We characterize such symbols, as well as the class of symbols for whichT
a
=0 impliesa(r)=0 a.e. For each compact setM there exists a Toeplitz operatorT
a
such that spT
a
=ess-spT
a
=M. We show that the set of symbols which generate bounded Toeplitz operators no longer forms an algebra under pointwise multiplication.Besides the algebra of Toeplitz operators we consider the algebra of Weyl pseudodifferential operators obtained from Toeplitz ones by means of the Bargmann transform. Rewriting our Toeplitz and Weyl pseudodifferential operators in terms of the Wick symbols we come to their spectral decompositions.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
14.
广泛的意义下定义 Toeplitz 算子, 给出了Toeplitz 算子乘积仍为Toeplitz 算子的充分必要条件, Toeplitz算子是正规算子的充分必要条件以及 Toeplitz 算子可交换的一个必要条件,从而推广了经典 Toeplitz 算子的相应结果. 相似文献
15.
We study Toeplitz operators on the Fock space with positive measures as symbols. Main results include characterizations of
Fock–Carleson measures, bounded Toeplitz operators, compact Toeplitz operators, and Toeplitz operators in the Schatten p-classes. 相似文献
16.
In this paper, we first investigate the finite-rank product problem of several Toeplitz operators with quasihomogeneous symbols on the harmonic Bergman space. Next, we characterize finite rank commutators and semi-commutators of two Toeplitz operators with quasihomogeneous symbols. 相似文献
17.
In this paper,we discuss some algebraic properties of Toeplitz operators and small Hankel operators with radial and quasihomogeneous symbols on the harmonic Bergman space of the unit disk in the complex plane C.We solve the product problem of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator.Meanwhile,we characterize the commutativity of quasihomogeneous Toeplitz operator and quasihomogeneous small Hankel operator. 相似文献
18.
In this paper, the product and commutativity of slant Toeplitz operators are discussed. We show that the product of kth1-order slant Toeplitz operators and kth2-order slant Toeplitz operators must be a (k1k2) th-order slant Toeplitz operator except for zero operators, and the commutativity and essential commutativity of two slant Toeplitz operators with different orders are the same. 相似文献
19.
In this paper, commutativity of kth‐order slant Toeplitz operators are discussed. We show that commutativity and essential commutativity of two slant Toeplitz operators are the same. Also, we study kth‐order slant Toeplitz operators on the Bergman space L2a(D) and give some commuting properties, algebraic and spectral properties of kth‐order slant Toeplitz operators on the Bergman space (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
On the Dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the Dirichlet space and their analogues defined on the Hardy space. Based on this, we characterize when finite sums of products of Toeplitz operators are of finite rank. Also, we give a necessary and sufficient condition for the commutator and semi-commutator of two Toeplitz operators being zero. 相似文献