Similarity of multiplication operators on the Sobolev disk algebra

In this paper, we give a similarity classification for the multiplication operator M _g on the Sobolev disk algebra $R(\mathbb{D})$ with g analytic on the closure of the unit disk $\mathbb{D}$ .     

Multiplication operators on sobolev disk algebra

In this paper,we study the algebra consisting of analytic functions in the Sobolev space W~(2,2) (D) (D is the unit disk),called the Sobolev disk algebra,explore the properties of the multiplication operators M_f on it and give the characterization of the corn- mutant algebra A′(M_f) of M_f.We show that A′(M_f) is commutative if and only if M_f~* is a Cowen-Douglas operator of index 1.     

Weighted composition operators between Dirichlet spaces

In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces.     

WEIGHTED COMPOSITION OPERATORS BETWEEN BERS-TYPE SPACES AND BERGMAN SPACES

This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space （or little Bers-type space） and Bergman space. Some estimates for the norm of weighted composition operators between those spaces are obtained.     

Numerical ranges of weighted composition operators

The operator that takes the function f   to ψf°φ$\psi f°\phi$ is a weighted composition operator. We study numerical ranges of some classes of weighted composition operators on H²$H^2$, the Hardy–Hilbert space of the unit disc. We consider the case where φ is a rotation of the unit disc and identify a class of convexoid operators. In the case of isometric weighted composition operators we give a complete classification of their numerical ranges. We also consider the inclusion of zero in the interior of the numerical range.     

Finite Blaschke product and the multiplication operators on Sobolev disk algebra

Let R(D) be the algebra generated in Sobolev space W22(D) by the rational functions with poles outside the unit disk D. In this paper the multiplication operators Mg on R(D) is studied and it is proved that Mg ～ Mzn if and only if g is an n-Blaschke product. Furthermore, if g is an n-Blaschke product, then Mg has uncountably many Banach reducing subspaces if and only if n > 1.     

Weighted composition operators and locally convex algebras

The Gleason-Kahane-Zelazko theorem characterizes the continuous homo-morphism of an associative, locally multiplicatively convex, sequentially complete algebra A into the field C among all linear forms on A. This characterization will be applied along two different directions. In the case in which A is a commutative Banach algebra, the theorem yields the representation of some classes of continuous linear maps A:A→A as weighted composition operators, or as composition operators when A is a continuous algebra endomorphism. The theorem will then be applied to explore the behaviour of continuous linear forms on quasi-regular elements, when A is either the algebra of all Hilbert-Schmidt operators or a Hilbert algebra.     

Weighted composition operators on the Hilbert space of Dirichlet series

In this paper, we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients. The Hermitianness, Fredholmness and invertibility of such operators are characterized, and the spectra of compact and invertible weighted composition operators are also described.     

加权复合算子的不变测度

本文研究复的可分 Hilbert L2 ( S,Σ,μ)加权复合算子 Tf(· ) =w(· ) f( h(· ) )存在平方可积的不变测度的条件 ,并且证明关于 T不变的平方可积的测度支集全体所张成的闭子空间等于 T的幺模特征向量全体所张成的闭子空间     

Aluthge transforms of unbounded weighted composition operators in L2-spaces

We describe the Aluthge transform of an unbounded weighted composition operator acting in an L²-space. We show that its closure is also a weighted composition operator with the same symbol and a modified weight function. We investigate its dense definiteness. We characterize p-hyponormality of unbounded weighted composition operators and provide results on how it is affected by the Aluthge transformation. We show that the only fixed points of the Aluthge transformation on weighted composition operators are quasinormal ones.     

Weighted composition operators from Bergman-type spaces into Bloch spaces

Let ϕ be an analytic self-map and u be a fixed analytic function on the open unit disk D in the complex plane ℂ. The weighted composition operator is defined by

解析函数空间上的自伴加权复合算子

通过再生核函数刻画了Hardy空间,Bergman空间上自伴加权复合算子以及自伴等距加权复合算子,最后研究了单位球上的分式线性自同构,得到了一个充分条件。     

WEIGHTED APPROXIMATION ON SZASZ—TYPE OPERATORS

In this paper, we use weighted modules ω(?)(f,t)w to study the pointwise approximation on Szasz-type operators, and obtain the direct and converse theorem, as well as characterizations of the pointwise approximation of Jacobi-weighted Szasz-type operators.     

对称Fock空间上的加权复合算子

本文研究了可分Hilbert空间上的对称Fock空间上有界(线性和反线性)加权复合算子. 完全刻画了酉加权复合算子和自伴加权复合算子, 并考虑了一类正规加权复合算子.     

Besov空间到Zygmund空间上的加权复合算子

研究了单位圆盘上的Besov空间B_(p,q)到Zygmund空间Z的加权复合算子u C_φ(u∈Z),利用函数空间上的算子理论相关知识,得到了u C_φ:B_(p,q)→Z的有界性和紧性的充分必要条件.     

Lipschitz空间上的加权复合算子

设D是复空间C中的单位圆盘,ψ是D到自身的一个全纯映射,ψ(z)是D上的全纯函数,0＜α＜1.本文给出了单位圆盘中Lipschitz空间Lipa(D)上由ψ和ψ诱导的加权复合算子Wψ,ψ的有界性及紧性的充要条件.