Toeplitz operators on H~2(iR)

In this paper,the essential spectra of Toeplitz operators is discussed,and the K-theory of the Toeplitz algebra generated by {Tφ|φ∈C(iR)} is computed.In addition,the characteristic equation of Toeplitz operators is obtained and the algebraic properties of Toeplitz operators are discussed.     

TOEPLITZ OPERATORS ON HEISENBERG GROUP

Denote by Ω the Siegel domain in Cn, n 〉 1. In this paper, we study the essential spectra of Toeplitz operators defined on the Hardy space H2（а↓Ω）. In addition, the characteristic equation of analytic Toeplitz operators iааs obtained.     

斜Toeplitz算子的乘积和交换性

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.     

Toeplitz Products on Bergman–Sobolev Spaces over the Unit Polydisk

In this paper, we characterize the compactness and Fredholmness of Toeplitz operators and Toeplitz products on Bergman–Sobolev spaces over the unit polydisk. We also calculate the essential norm of finite sums of finite Toeplitz products on these spaces.     

ON GRAPH MEASURES IN BANACH SPACES AND DESCRIPTION OF ESSENTIAL SPECTRA OF MULTIDIMENSIONAL TRANSPORT EQUATION

In this paper,we define new measures called respectively graph measure of noncompactness and graph measure of weak noncompactness.Moreover,we apply the obtained results to discuss the incidence of some perturbation results realized in [2] on the behavior of essential spectra of such closed densely defined linear operators on Banach spaces.These results are exploited to investigate the essential spectra of a multidimensional neutron transport operator on L1 spaces.     

Dual Toeplitz operators on the sphere

Dual Toeplitz operators on the Hardy space of the unit circle are anti-unitarily equivalent to Toeplitz operators. In higher dimensions, for instance on the unit sphere, dual Toeplitz operators might behave quite differently and, therefore, seem to be a worth studying new class of Toeplitz-type operators. The purpose of this paper is to introduce and start a systematic investigation of dual Toeplitz operators on the orthogonal complement of the Hardy space of the unit sphere in Cn . In particular, we establish a corresponding spectral inclusion theorem and a Brown-Halmos type theorem. On the other hand, we characterize commuting dual Toeplitz operators as well as normal and quasinormal ones.     

单位球Dirichlet空间上以拟齐次函数为符号的Toeplitz算子

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.     

TOEPLITZ OPERATORS FROM HARDY SPACES TO WEIGHTED BERGMAN SPACES IN THE UNIT BALL OF Cn

We study Toeplitz operators from Hardy spaces to weighted Bergman spaces in the unit ball of Cⁿ.Toeplitz operators are closely related to many classical mappings,such as composition operators,the Volterra type integration operators and Carleson embeddings.We characterize the boundedness and compactness of Toeplitz operators from Hardy spaces H^p to weighted Bergman spaces A_α^q for the different values of p and q in the unit ball.     

TOEPLITZ OPERATORS WITH POSITIVE OPERATOR-VALUED SYMBOLS ON VECTOR-VALUED GENERALIZED FOCK SPACES

In this article, we study some characterizations of Toeplitz operators with positive operator-valued function as symbols on the vector-valued generalized Bargmann-Fock spaces F_φ~2. Main results including Fock-Carleson condition, bounded Toeplitz operators, compact Toeplitz operators, and Toeplitz operators in the Schatten-p class are all considered.     

Toeplitz operators on Fock-Sobolev spaces with positive measure symbols

We discuss Toeplitz operators on Fock-Sobolev space with positive measure symbols.By FockCarleson measure,we obtain the characterizations for boundedness and compactness of Toeplitz operators.We also give some equivalent conditions of Schatten p-class properties of Toeplitz operators by Berezin transform.     

有界连通区域上Dirichlet空间及其算子

本文主要讨论了有界连通区域Dirichlet空间上Toeplitz算子的Fredholm性质,计算了符号在C1中的Toeplitz算子的本性谱和Fredholm指标．     

H~2(S)上Toeplitz算子本质谱的局部分解

本文利用Ｂａｎａｃｈ代数中局部化原理给出了多复变Ｈａｒｄｙ空间上Ｔｏｅｐｌｉｔｚ算子是Ｆｒｅｄｈｏｌｍ算子的一个充分必要条件；同时给出了Ｔｏｅｐｌｉｔｚ算子本质谱的局部分解．     

圆环上的Dirichlet空间及其算子

本文主要讨论了圆环上Dirichlet空间中Toeplitz算子的Fredholm性质,计算了符号在C~1和H_1~∞+C~1中的Toeplitz算子的本性谱.     

Bergman空间上Toeplitz算子的局部及Fredholm性质

本文讨论了Ｂｅｒｇｍａｎ空间上Ｔｏｅｐｌｉｔｚ算子的局部谱的关系．利用局部化原理给出了Ｔｏｅｐｌｉｔｚ算子拟换位子紧性的一个充分条件．给出了一类符号的Ｔｏｅｐｌｉｔｚ算子是Ｆｒｅｄｈｏｌｍ算子的充分条件．     

Toeplitz and composition operators on H2 (B n)

The composition operators with closed rangc on H²(B _n) are characterized, and the Fredholmness of products of Toeplitz and composition operators discussed. Moreover, using composition operators, the spectra of Toeplitz operators are studied. Project supported by the National Natural Sciencc Foundation of China and the Postdoctoral Science Foundation of China.     

Computing the Fredholm index of Toeplitz operators with continuous symbols

We show how to compute the Fredholm index of a Toeplitz operator with a continuous symbol constructed from any subnormal operator with compact self-commutator. We also show that the essential spectral pictures of such Toeplitz operators can be prescribed arbitrarily.

     

TOEPLITZ OPERATORS AND ALGEBRAS ON DIRICHLET SPACES

The automorphism group of the Toeplitz C-algebra,J(C~1),generated by Toeplitz op-erators with C~1-symbols on Dirichlet space D is discussed;the K_0,X_1-groups and the firstcohomology group of J(C~1)are computed.In addition,the author provs that the spectraof Toeplitz operators with C~1-symbols are always connected,and discusses the algebraic prop-erties of Toeplitz operators.In particular,it is proved that there is no nontrivial selfadjointToeplitz operator on D and T_φ~*=T_φ if and only if T_φ is a scalar operator.     

多重圆盘上的Toeplitz代数

本文研究了H~2(T~n)上由符号为本性有界可测函数的Toeplitz算子生成的C~*-代数的结构,并得到了这样的Toeplitz算子的一些谱性质.