Hibert空间中广义框架的非交性

引入了Hilbert空间H中广义框架的非交性、强非交性,讨论了它们的一些性质;并且引入了保非交算子、强保非交算子,证明了酉算子、可逆算子是强保非交算子,下有界算子、余等距算子是保非交算子.     

有界线性算子的(h)性质和(gh)性质

研究了有界线性算子的(h)性质和(gh)性质的问题.利用算子的单值扩张性的方法,获得了Banach空间上有界线性算子的(h)性质和(gh)性质的几个充分必要条件以及它们与其他Weyl型定理之间的关系,(h)性质和(gh)性质是a-Weyl定理和广义a-Weyl定理的推广.     

严格循环的算子代数

设X是半自共轭的Banach空间,而A是B(X)的严格循环的交换子代数,考虑算子代数A的一些性质,这些性质与算子代数的自反性有关,而且这些性质为讨论A的自反性提供了理论基础.     

单位球上的对偶Toeplitz算子

本文研究了单位球Bergman空间的直交补上的对偶Toeplitz算子的代数性质,首先我们给出了对偶Toeplitz算子的有界性和紧性的完全刻画,然后给出对偶Toeplitz算子的谱性质,最后证明了不存在以有界全纯或者反全纯函数为符号的拟正规对偶Toeplitz算子.     

Clifford分析中具有超正则核的T算子的性质

讨论了Clifford分析中具有超正则核的T(Ieodorescu)算子的基本性质.T算子是定义在区域上的奇异积分算子,它在广义解析函数理论和Vekua理论中起着重要的作用.在复分析中关于T算子的理论已经发展得很完善,但在Clifford分析中,具有超正则核的T算子的相关性质还没有得到研究.研究了Clifford分析中具有超正则核的T算子的基本性质,得到了这个算子在ΩR_+~(n+1)上的一致有界性,Hlder连续性以及这个算子的γ次可积性.     

关于Lipschitz映射空间的可余子空间

该文研究Lipschitz映射空间作为一个Banach空间的结构性质，主要研究了它的闭子空间有界线性算子空间（赋予算子范数）在其中的可余性．     

Dirichlet空间上Toeplitz算子的亚正规性

讨论单位圆盘中Dirichlet空间上Toeplitz算子的性质,给出了Dirichiet空间上以一类连续函数为符号的Toeplitz算子满足亚正规性的充分必要条件．     

Dirichlet空间上Toeplitz算子的一些性质

该文研究了Dirichlet空间D^p~(1< p<∞)上Toeplitz算子的紧性与Fredholm性质, 计算了D^p上Toeplitz算子的Fredholm指标. 还考查了D^p上Hankel算子紧性.     

L_([0,1])~p空间具可测核的积分算子的性质

主要在L_([0,1])~p空间中研究核为可测函数的积分算子的性质.通过运用泛函分析的相关知识得到当p1时,积分算子为紧线性算子的结论,进而验证了积分算子的共轭算子为L_([0,1])~q空间中的紧线性算子.     

一类积-微分算子根子空间完备性问题的研究

讨论了迁移理论中出现的一类积-微分算子,利用拟占优本征函数的性质,证明了这类算子本征值的根子空间的不完备性。     

BANDED TOEPLITZ PRECONDITIONERS FOR TOEPLITZ MATRICES FROM SINC METHODS

We give general expressions, analyze algebraic properties and derive eigenvalue bounds for a sequence of Toeplitz matrices associated with the sinc discretizations of various orders of differential operators. We demonstrate that these Toeplitz matrices can be satisfactorily preconditioned by certain banded Toeplitz matrices through showing that the spectra of the preconditioned matrices are uniformly bounded. In particular, we also derive eigenvalue bounds for the banded Toeplitz preconditioners. These results are elementary in constructing high-quality structured preconditioners for the systems of linear equations arising from the sinc discretizations of ordinary and partial differential equations, and are useful in analyzing algebraic properties and deriving eigenvalue bounds for the corresponding preconditioned matrices. Numerical examples are given to show effectiveness of the banded Toeplitz preconditioners.     

Algebraic Properties of Toeplitz Operators on the Harmonic Dirichlet Space

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.     

Fock空间上的对偶Toeplitz代数

通过符号映射研究Fock空间之正交补空间上对偶Toeplitz代数的结构,得到了Fock空间上对偶Toeplitz代数的一个短正合序列.并研究了对偶Toeplitz算子谱的性质.     

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.     

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．     

COMPLEX SYMMETRIC TOEPLITZ OPERATORS ON THE UNIT POLYDISK AND THE UNIT BALL

In this article, we study complex symmetric Toeplitz operators on the Bergman space and the pluriharmonic Bergman space in several variables. Surprisingly, the necessary and sufficient conditions for Toeplitz operators to be complex symmetric on these two spaces with certain conjugations are just the same. Also, some interesting symmetry properties of complex symmetric Toeplitz operators are obtained.     

Properties of Toeplitz Operators on the Dirichlet Space Over the Ball

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.     

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.     

Asymptotic Toeplitz and Hankel operators on the Bergman space

In this paper the concept of asymptotic Toeplitz and asymptotic Hankel operators on the Bergman space are introduced and properties of these classes of operators are studied. The importance of this notion is that it associates with a class of operators a Toeplitz operator and with a class of operators a Hankel operator where the original operators are not even Toeplitz or Hankel. Thus it is possible to assign a symbol to an operator that is not Toeplitz or Hankel and hence a symbol calculus is obtained. Further a relation between Toeplitz operators and little Hankel operators on the Bergman space is established in some asymptotic sense.