Numerical range of Weighted Composition Operator on $ML^2(\mathbb{C};q)$

Weighted composition operators on weak vector-valued weighted Bergman spaces and Hardy spaces

In this paper we investigate weighted composition operators between weak and strong vector valued weighted Bergman spaces and Hardy spaces.

Weighted composition operators on the Fock space

In this paper, we study weighted composition operators on the Fock space. We show that a weighted composition operator is cohyponorma if and only if it is normal. Moreover, we give a complete characterization of closed range weighted composition operators. Finally, we find norms of some weighted composition operators.

Hyperexpansive weighted composition operators

In this note unbounded hyperexpansive weighted composition operators are investigated. AS a consequence unbounded hyperexpansive multiplication and composition operators are characterized.

The weighted composition operators on the large weighted Bergman spaces

In this paper, we characterize bounded, compact or Schatten class weighted composition operators acting on Bergman spaces with the exponential type weights. Moreover, we give the proof of the necessary part for the boundedness of composition operators on large weighted Bergman spaces given by Kriete and Maccluer in 1992.

Complex symmetric weighted composition operators

In this paper we find all complex symmetric weighted composition operators with special conjugations. Then we give spectral properties of these complex symmetric weighted composition operators.

Self-adjoint, unitary, and normal weighted composition operators in several variables

We study weighted composition operators on Hilbert spaces of analytic functions on the unit ball with kernels of the form $(1-<z,w>)^{-γ}$ for $γ>0$. We find necessary and sufficient conditions for the adjoint of a weighted composition operator to be a weighted composition operator or the inverse of a weighted composition operator. We then obtain characterizations of self-adjoint and unitary weighted composition operators. Normality of these operators is also investigated.

Weighted composition operators on discrete weighted Banach spaces

We present the current results in the study of weighted composition operators on weighted Banach spaces of an unbounded, locally finite metric space. Specifically, we determine characterizations of bounded and compact weighted composition operators, including the operator and essential norms. In addition, we characterize the weighted composition operators that are injective, are bounded below, have closed range, and have bounded inverse. We characterize the isometries and surjective isometries among the weighted composition operators, as well as those that satisfy the Fredholm condition. Lastl…

Weighted composition operators acting from the Lipschitz space to the space of bounded functions on a tree

We study the weighted composition operators between the Lipschitz space and the space of bounded functions on the set of vertices of an infinite tree. We characterized the boundedness, the compactness, and the boundedness from below of weighted composition operators. We also determine the isometric weighted composition operators.

加权复合算子在加权狄里赫雷空间上的有界性、紧性及谱性质

Weighted composition operators on weighted Dirichlet spaces: boundedness, compactness and spectral properties

本文研究了加权复合算子在加权狄里赫雷空间上的有界性、紧性及谱性质，扩展了无权复合算子的研究成果。

Weighted composition operators from the Bloch space to weighted Banach spaces on bounded homogeneous domains

We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide computable estimates on the operator norm.

Weighted composition operators on Fock spaces and their dynamics

Bounded weighted composition operators, as well as compact weighted composition operators, on Fock spaces have been characterised. This characterisation is refined to the extent that the question of whether weighted composition operators on the Fock space can be supercyclic is answered in the negative.

Weighted composition, Volterra and Integral operators on Hardy Zygmund-type spaces

In this paper, we investigate weighted composition, Volterra and Integral operators on second derivative Hardy spaces. Some equivalent conditions for boundedness of the operators will be given using the boundedness on the Hardy spaces. Also we give a criteria for compactness of weighted composition operators.

Differences of weighted composition operators between the Fock spaces

We study some important topological properties such as boundedness, compactness and essential norm of differences of weighted composition operators between Fock spaces

L²空间中加权复合算子的倒数

Reciprocals of weighted composition operators in $L^2$-spaces

本文给出L²空间中稠定加权复合算子及其伴随算子的倒数公式，研究了该算子倒数与相关乘法算子和复合算子倒数乘积的关系。

加权福克空间上的加权复合算子

Weighted composition operators on weighted Fock spaces

该研究给出加权福克空间上加权复合算子有界、紧和希尔伯特-施密特类的刻画及本质范数估计，方法依赖米塔格-莱夫勒函数渐近行为，还建立指数权重加权复合算子准则并恢复复合算子相应结果。

加权Bergman空间上Toeplitz算子与复合算子的数值域

Numerical range of Toeplitz and Composition operators on weighted Bergman spaces

本文完整刻画了加权Bergman空间上调和符号Toeplitz算子及加权复合算子的数值域，分类了复合算子数值域对应的集合，并研究了零的包含性及所含圆和椭圆的半径。

Complex symmetric weighted composition operators on Dirichlet spaces and Hardy spaces in the unit ball

In this paper, we investigate when weighted composition operators acting on Dirichlet spaces $\mathcal{D}(\mathbb{B}_{N})$ are complex symmetric with respect to some special conjugations, and provide some characterizations of Hermitian weighted composition operators on $\mathcal{D}(\mathbb{B}_{N})$. Furthermore, we give a sufficient and necessary condition for $J$-symmetric weighted composition operators on Hardy spaces $H^2(\mathbb{B}_{N})$ to be unitary or Hermitian, then some new examples of complex symmetric weighted composition operators on $H^2(\mathbb{B}_{N})$ are obtained. We also disc…

Weighted composition operator on quaternionic Fock space

In this paper, we study the weighted composition operator on the Fock space $\mf$ of slice regular functions. First, we characterize the boundedness and compactness of the weighted composition operator. Subsequently, we describe all the isometric composition operators. Finally, we introduce a kind of (right)-anti-complex-linear weighted composition operator on $\mf$ and obtain some concrete forms such that this (right)-anti-linear weighted composition operator is a (right)-conjugation. Specially, we present equivalent conditions ensuring weighted composition operators which are conjugate $\mat…

加权复合算子在加权狄拉克空间上的数值范围与伯泽林范围

Numerical range and Berezin range of weighted composition operators on weighted Dirichlet spaces

本文研究加权复合算子在加权狄拉克空间上的数值范围与伯泽林范围，分析其几何结构及凸性，并计算相关半径和数。

Volterra-composition operators on the weighted Bergman space with exponential type weights

The properties of Volterra-composition operators on the weighted Bergman space with exponential type weights are investigated in this paper. We state some necessary and sufficient conditions that a Volterra-composition operator from the weighted Bergman space to Bloch type space ( or little Bloch type space ) must satisfy for the Volterra-composition operator to be bounded or compact.

A note on the complex symmetric weighted composition operators over Hardy space

This paper provides a class of complex symmetric weighted composition operators on $H^2(\mathbb{D})$ to includes the unitary subclass, the Hermitian subclass and the normal subclass obtained by Bourdon and Noor. A characterization of algebraic weighted composition operator with degree no more than two is provided to illustrate that the weight function of a complex symmetric weighted composition operator is not necessarily linear fractional. \end{abstract}

Isometric and invertible composition operators on weighted Bergman spaces of Dirichlet series

We show that a composition operator on weighted Bergman spaces $\mathcal{A}_μ^p$ is invertible if and only if it is Fredholm if and only if it is an isometry.

Spectra of weighted composition operators induced by automorphisms

In the paper we give the results about the spectra of non-invertible weighted composition operators induced by automorphisms on several Hilbert spaces, such as Hardy-Hilbert space $H^2(\mathbb{D})$ and weighted Bergman spaces $A_α^2(\mathbb{D})$.

Reproducing kernel Hilbert spaces supporting nontrivial Hermitian weighted composition operators

We characterize those generating functions k that produce weighted Hardy spaces of the unit disk D supporting nontrivial Hermitian weighted composition operators. Our characterization shows that the spaces associated with the "classical reproducing kernels," as well as certain natural extensions of these spaces, are precisely those that are hospitable to Hermitian weighted composition operators. It also leads to a refinement of a necessary condition for a weighted composition to be Hermitian, obtained recently by Cowen, Gunatillake, and Ko, into one that is both necessary and sufficient.

有向图上m-等距加权复合算子的扩张

Extension of m-isometric weighted composition operators on directed graphs

该研究针对含单回路、多分支顶点的有向图，探讨了k-拟-m-等距复合算子及加权复合算子相关内容，丰富了有向图上算子理论的研究范畴。

Composition operators acting on weighted Hilbert spaces of analytic functions

In this paper, we consider composition operators on weighted Hilbert spaces of analytic functions and observe that a formula for the essential norm, give a Hilbert-Schmidt characterization and characterize the membership in Schatten-class for these operators. Also, closed range composition operators are investigated.

Composition operators on weighted $L^{p}$ spaces of a tree

In this paper, we study the boundedness, compactness and Schatten class membership of composition operators on the weighted $L^{p}$-space of a tree $L^{p}_λ(T)$ with $1\leq p <\infty$.

Finite sum of weighted composition operators with closed range

In this paper, first we characterize closedness of range of the finite sum of weighted composition operators between different Lp-spaces. Then we discuss polar decomposition and invertibility of these operators.

Weighted Composition Operator and the Mittag-Leffler space

We present important characterizations of the Weighted Composition Operator over the Mittag Leffler space of entire functions. These characterizations include the Hilbert-Schmidt and Unitary char-acterizations of the Weighted Composition Operator over the Mittag-Leffler space. We also see the result for the spectrum of Weighted com-position operator over the Mittag-Leffler space

Weighted Composition--Differentiation Operator on the Hardy and Weighted Bergman Spaces

In this paper, we consider the sum of weighted composition operator $C_{ψ_{0},φ_{0}}$ and the weighted composition--differentiation operator $D_{ψ_{n},φ_{n},n}$ on the Hardy and weighted Bergman spaces. We describe the spectrum of a compact operator $C_{ψ_{0},φ_{0}}+D_{ψ_{n},φ_{n},n}$ when the fixed point $w$ of $φ_{0}$ and $φ_{n}$ is inside the open unit disk and $ψ_{n}$ has a zero at $w$ of order at least $n$. Also the lower estimate and the upper estimate on the norm of a weighted composition--differentiation operator on the Hardy space $H^{2}$ are obtained. Furthermore, we determine the no…

Normal, cohyponormal and normaloid weighted composition operators on the Hardy and weighted Bergman spaces

If $ψ$ is analytic on the open unit disk $\mathbb{D}$ and $φ$ is an analytic self-map of $\mathbb{D}$, the weighted composition operator $C_{ψ,φ}$ is defined by $C_{ψ,φ}f(z)=ψ(z)f (φ(z))$, when $f$ is analytic on $\mathbb{D}$. In this paper, we study normal, cohyponormal, hyponormal and normaloid weighted composition operators on the Hardy and weighted Bergman spaces. First, for some weighted Hardy spaces $H^{2}(β)$, we prove that if $C_{ψ,φ}$ is cohyponormal on $H^{2}(β)$, then $ψ$ never vanishes on $\mathbb{D}$ and $φ$ is univalent, when $ψ\not \equiv 0$ and $φ$ is not a constant function. M…

Fock空间上复对称加权复合算子的交换子

Commutants of complex symmetric weighted composition operators on Fock space

本文研究经典Fock空间上加权复合算子与复对称加权复合算子可交换的条件，并刻画可交换算子自伴和正规的充要条件。

超几何复合运算和加权复合半群生成元的谱

Spectra of generators of hyperbolic composition and weighted composition semigroups

本文研究了由超几何半流在贝格曼空间上诱导的加权复合$C_0$-半群生成元的谱、本质谱和点谱的完整刻画，并通过一个例子展示了半群在非固定自接触点附近的行为如何影响谱性质。

Weighted composition operators as Daugavet centers

We investigate the norm identity $\|uC_ϕ+ T\| = \|u\|_\infty + \|T\|$ for classes of operators on $C(S)$, where $S$ is a compact Hausdorff space without isolated point, and characterize those weighted composition operators which satisfy this equation for every weakly compact operator $T : C(S)\to C(S)$. We also give a characterization of such weighted composition operator acting on the disk algebra $A(D).$

一类其值域空间与零空间是补子空间的加权复合算子

A class of weighted composition operators whose Range and Null spaces are complemented

本文证明了 $\ell_p$ 上加权复合算子的零空间是补子空间，给出了值域空间具有限余维数的充要条件，并刻画了值域为补子空间及 Fredholm 算子的加权复合算子类。

Spectrum of Weighted Composition Operators. Part V. Spectrum and essential spectra of weighted rotation-like operators

We introduce the class of weighted "rotation-like" operators and study general properties of essential spectra of such operators. Then we use this approach to investigate and in some cases completely describe essential spectra of weighted rotation operators in Banach spaces of measurable and analytic functions.

Complex symmetric weighted Composition Differentiation Operators

In this note, we completely characterize complex symmetric weighted composition differentiation operator on the Hardy space $H^2$ with respect to the conjugation operator $C_{λ,α}$. Meanwhile, the normal and self-adjoint of the weighted composition differentiation operators on the Hardy space $H^2$ are also studied. This note could be considered as a continuation of the work initiated by Fatehi and Hammond.

New characterizations for the essential norms of generalized weighted composition operators between Zygmund type spaces

We give different types of new characterizations for the boundedness and essential norms of generalized weighted composition operators between Zygmund type spaces. Consequently, we obtain new characterizations for the compactness of such operators.

Unbounded Weighted Composition Operators in L2-Spaces

Bounded and unbounded weighted composition operators on $L^2$ spaces over $σ$-finite measure spaces are investigated. A variety of questions related to seminormality of such operators are discussed.

$L^2$空间中无界加权复合算子的Aluthge变换

Aluthge transforms of unbounded weighted composition operators in $L^2$-spaces

本文研究$L^2$空间中无界加权复合算子的Aluthge变换，揭示其闭包的算子结构、稠密有定性，刻画$p$-亚正规性及变换对其的影响，证明拟正规算子是该变换的唯一不动点。

Composition operators on weighted Banach spaces of a tree

We study composition operators on the weighted Banach spaces of an infinite tree. We characterize the bounded and the compact operators, as well as determine the operator norm and the essential norm. In addition, we study the isometric composition operators.

Weighted composition operators of $C_0(X)$'s

In this paper, we prove that into isometries and disjointness preserving linear maps from $C_0(X)$ into $C_0(Y)$ are essentially weighted composition operators $Tf = h\cdot f\circφ$ for some continuous map $φ$ and some continuous scalar-valued function $h$.

Composition operators on weighted Bergman spaces of Dirichlet series

We study boundedness and compactness of composition operators on weighted Bergman spaces of Dirichlet series. Particularly, we obtain in some specific cases, upper and lower bounds of the essential norm of these operators and a criterion of compactness on classicals weighted Bergman spaces. Moreover, a sufficient condition of compactness is obtained using the notion of Carleson's measure.

关于狄里赫利空间上加权复合算子的注记

A note on weighted composition operators on Dirichlet space

本文研究了狄里赫利空间上加权复合算子的紧性条件、数值范围刻画及零点包含准则，并引入了具有特定数值范围的算子类。

Quasinormal extensions of subnormal operator-weighted composition operators in $\ell^2$-spaces

We prove the subnormality of an operator-weighted composition operator whose symbol is a transformation of a discrete measure space and weights are multiplication operators in $L^2$-spaces under the assumption of existence of a family of probability measures whose Radon-Nikodym derivatives behave regular along the trajectories of the symbol. We build the quasinormal extension which is a weighted composition operator induced by the same symbol. We give auxiliary results concerning commutativity of operator-weighted composition operators with multiplication operators.

加权复合算子的谱。第十部分。多圆盘代数加权自同构的谱与本质谱

Spectrum of Weighted Composition Operators. Part X. The spectrum and essential spectra of weighted automorphisms of the polydisc algebra

本文研究了多圆盘代数加权自同构的谱与本质谱，并在二维情形下给出了这些谱的详细且多数情况下完整的描述。

Weighted composition operators: isometries and asymptotic behaviour

This paper studies the behaviour of iterates of weighted composition operators acting on spaces of analytic functions, with particular emphasis on the Hardy space $H^2$. Questions relating to uniform, strong and weak convergence are resolved in many cases. Connected to this is the question when a weighted composition operators is an isometry, and new results are given in the case of the Hardy and Bergman spaces.

The essential norm of a weighted composition operator on BMOA

We provide an estimate for the essential norm of a weighted composition operator $W_{ψ,φ}\colon f\mapsto ψ(f\circφ)$ acting on the space $BMOA$ in terms of the weight function $ψ$ and the $n$-th power $φ^n$ of the analytic self-map $φ$ of the open unit disc $\mathbb{D}$. We also provide a new estimate for the norm of the weighted composition operator on $BMOA$.

$L^2$空间中的弱中心加权复合算子

Weakly centered weighted composition operators in $L^2$-spaces

该研究刻画了$L^2$空间中的弱中心及谱弱中心加权复合算子，给出不变子空间存在性的判别准则，并补充了相关结果与示例。

Stability for weighted composition $C_0$-semigroups on Lebesgue and Sobolev spaces

Stability of weighted composition strongly continuous semigroups acting on Lebesgue and Sobolev spaces is studied, without the use of spectral conditions on the generator of the semigroup. Applications to the generalized von Foerster - Lasota semigroup and a comparison with hypercylicity conditions are presented.\

Weighted composition operators on the class of subordinate functions

In this article, we study the weighted composition operators preserving the class $\mathcal{P}_α$ of analytic functions subordinate to $\frac{1+αz}{1-z}$ for $|α|\leq 1, α\neq -1$. Some of its consequences and examples for some special cases are presented. Furthermore, we discuss about the fixed points of weighted composition operators.

Spectra of Weighted Composition Operators with Quadratic Symbols

Previously, spectra of certain weighted composition operators on the Hardy Space were discovered under one of two hypotheses: either the compositional symbol converges under iteration to the Denjoy-Wolff point on all of the open disk rather than compact subsets, or the compositional symbol is "essentially linear fractional". We show that if the symbol is a quadratic self-map of the disk of parabolic type, then the spectrum of the weighted composition operators can be found when these maps exhibit both of the aforementioned properties, and most of them do.

关于 $L^2$-空间上中心加权复合算子的再审视

Centered weighted composition operators on $L^2$-spaces revisited

本文重新研究了 $L^2$-空间上的中心加权复合算子，提出了半谱中心算子的概念，并给出了无界加权复合算子的条件及有向树上中心加权移位算子的判据。

Hypercyclicity of composition operators on discrete weighted Banach spaces

In this paper, we study the hypercyclic composition operators on weighted Banach spaces of functions defined on discrete metric spaces. We show that the only such composition operators act on the "little" spaces. We characterize the bounded composition operators on the little spaces, as well as provide various necessary conditions for hypercyclicity.