Some examples of compact composition operators on $H^2$

Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces

It is known, from results of B. MacCluer and J. Shapiro (1986), that every composition operator which is compact on the Hardy space $H^p$, $1 \leq p < \infty$, is also compact on the Bergman space ${\mathfrak B}^p = L^p_a (\D)$. In this survey, after having described the above known results, we consider Hardy-Orlicz $H^Ψ$ and Bergman-Orlicz ${\mathfrak B}^Ψ$ spaces, characterize the compactness of their composition operators, and show that there exist Orlicz functions for which there are composition operators which are compact on $H^Ψ$ but not on ${\mathfrak B}^Ψ$.

Compact composition operators on $H^2$ and Hardy-Orlicz spaces

We compare the compactness of composition operators on $H^2$ and on Orlicz-Hardy spaces $H^Ψ$. We show in particular that exists an Orlicz function $Ψ$ such that $H^{3+\eps} \subseteq H^Ψ\subseteq H^3$ for every $\eps >0$, and a composition operator $C_ϕ$ which is compact on $H^3$ and on $H^{3+\eps}$, but not compact on $H^Ψ$.

Spectrum of Weighted Composition Operators Part VII Essential spectra of weighted composition operators on $C(K)$. The case of non-invertible homeomorphisms

We provide a complete description of the spectrum and the essential spectra of weighted composition operators $T=wT_φ$ on $C(K)$ in the case when the map $φ$ is a non-invertible homeomorphism of $K$ into itself.

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.

Composition operators on Harmonic Bloch-type spaces

In this paper we consider composition operators on Harmonic-Bloch type spaces and we compute the spectrum of composition operators. Also, we characterize isometric composition operators on harmonic Bloch type spaces.

Product isometry of generalized weighted composition operator on general weighted Hardy space

We obtain necessary and sufficient conditions for the composition and weighted composition operator and product of composition operators to be isometry and unitary on $H_{E}(ξ).$ With the help of counter example we also prove that the product of two non isometric composition operator and weighted composition operator can be isometry on $H_{E}(ξ)$. We also completely characterize the boundedness of generalized weighted composition operators on $H_{E}(ξ).$

On Unbounded Composition Operators in $L^2$-Spaces

Fundamental properties of unbounded composition operators in $L^2$-spaces are studied. Characterizations of normal and quasinormal composition operators are provided. Formally normal composition operators are shown to be normal. Composition operators generating Stieltjes moment sequences are completely characterized. The unbounded counterparts of the celebrated Lambert's characterizations of subnormality of bounded composition operators are shown to be false. Various illustrative examples are supplied.

Distances between composition operators

The norm distance between two composition operators is calculated in select cases.

Spectrum of Weighted Composition Operators. Part II. Weighted composition operators on subspaces of Banach lattices

We describe the spectrum of weighted $d$-isomorphisms of Banach lattices restricted on closed subspaces that are "rich" enough to preserve some "memory" of the order structure of the original lattice. The examples include (but are not limited to) weighted isometries of Hardy spaces on the polydisk and unit ball in $\mathds{C}^n$.

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.

Compact composition operators on Hardy-Orlicz and weighted Bergman-Orlicz spaces on the ball

Using recent characterizations of the compactness of composition operators on Hardy-Orlicz and Bergman-Orlicz spaces on the ball, we first show that a composition operator which is compact on every Hardy-Orlicz (or Bergman-Orlicz) space has to be compact on H^{\infty}. Then, we prove that, for each Koranyi region Γ, there exists a map ϕtaking the ball into Γsuch that, C_ϕ is not compact on H^ψ\left(\mathbb{B}_{N}\right), when ψgrows fast. Finally, we give another characterization of the compactness of composition operator on weighted Bergman-Orlicz spaces in terms of an Orlicz "Angular derivat…

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.

Bounded composition operator on Lorentz spaces

We study a composition operator on Lorentz spaces. In particular we provide necessary and sufficient conditions under which a measurable mapping induces a bounded composition operator.

希尔伯特空间中非紧线性算子复合中的反常不适定现象

Curious ill-posedness phenomena in the composition of non-compact linear operators in Hilbert spaces

该研究探讨希尔伯特空间中非紧线性算子复合的不适定特性，分析典型算子及其组合的性质，给出特定算子复合的奇异值衰减估计，发现非紧算子复合为紧算子的实例并刻画相关算子特征。

Composition operators between two different bilateral grand Lebesgue spaces

In this paper we consider composition operator generated by nonsingular measurable transformation between two different Grand Lebesgue Spaces (GLS); we investigate the boundedness, compactness and essential norm of composition operators.

Common hypercyclic vectors for composition operators

We study the existence of a common hypercyclic vector for different families of composition operators.

On normal, formally normal and quasinormal composition operators in $\ell^2$-spaces

Unbounded composition operators in $L^2$-space over discrete measure spaces are investigated. Normal, formally normal and quasinormal composition operators acting in $L^2$-spaces of this kind are characterized.

Compact composition operators on Bergman-Orlicz spaces

We construct an analytic self-map $ϕ$ of the unit disk and an Orlicz function $Ψ$ for which the composition operator of symbol $ϕ$ is compact on the Hardy-Orlicz space $H^Ψ$, but not compact on the Bergman-Orlicz space ${\mathfrak B}^Ψ$. For that, we first prove a Carleson embedding theorem, and then characterize the compactness of composition operators on Bergman-Orlicz spaces, in terms of Carleson function (of order 2). We show that this Carleson function is equivalent to the Nevanlinna counting function of order 2.

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。

Composition operators on the Schwartz space

We study composition operators on the Schwartz space of rapidly decreasing functions. We prove that such a composition operator is never a compact operator and we obtain necessary or sufficient conditions for the range of the composition operator to be closed. These conditions are expressed in terms of multipliers for the Schwartz class and the closed range property of the corresponding operator considered in the space of smooth functions.

Composition operators on spaces of double Dirichlet series

We study composition operators on spaces of double Dirichlet series, focusing our interest on the characterization of the composition operators of the space of bounded double Dirichlet series $\HCdos$. We also show how the composition operators of this space of Dirichlet series are related to the composition operators of the corresponding spaces of holomorphic functions. Finally, we give a characterization of the superposition operators in $\HC$ and in the spaces $\mathcal{H}^p$.

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.

Essential norm of composition operators Harmonic Bloch spaces

In this paper we characterize essential norm of composition operators on the spaces of Harmonic Bloch functions. These results extends the similar results that were proven for composition operators on Bloch spaces.

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。

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.

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.

Compact and weakly compact composition operators from the Bloch space into Möbius invariant spaces

We obtain exhaustive results and treat in a unified way the question of boundedness, compactness, and weak compactness of composition operators from the Bloch space into any space from a large family of conformally invariant spaces that includes the classical spaces like $BMOA$, $Q_α$, and analytic Besov spaces $B^p$. In particular, by combining techniques from both complex and functional analysis, we prove that in this setting weak compactness is equivalent to compactness. For the operators into the corresponding "small" spaces we also characterize the boundedness and show that it is equivale…

复值调和函数希尔伯特空间上的有界复合算子

Bounded Composition Operators on Hilbert Space of Complex-Valued Harmonic Functions

本文研究复值调和函数希尔伯特空间上的复合算子，刻画了其有界性、等距性与生成自映射类型，并建立其与再生核的关系。

Compact differences of composition operators on large weighted Bergman spaces

While there have been extensive studies regarding the theory of composition operators in standard Bergman spaces, there have not been many results pertaining to large Bergman spaces due to a lack of useful tools. In this paper, we give the characterizations of the compact differences of composition operators in Bergman spaces with the exponential type weight using a newly defined Riemannian distance. Furthermore, we give a sufficient condition for the question when two composition operators lie in the same component.

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, 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.

On composition operators on the Wiener algebra of Dirichlet series

We show that the symbol of a bounded composition operator on the Wiener algebra of Dirichlet series does not need to belong to this algebra. Our example even gives an absolutely summing (hence compact) composition operator.

Approximation numbers of composition operators on Hp

We give estimates for the approximation numbers of composition operators on the Hp spaces, 1 $\le$ p \textless{} $\infty$.

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.

Products of composition and differentiation operators on the Hardy space

We consider the products of composition and differentiation operators on the Hardy space. We provide a complete characterization of the boundedness and compactness of these operators. Furthermore, we obtain the explicit condition for these operators to be Hilbert-Schmidt operators.

Spectrum of weighted composition operators. Part VIII. Lower semi-Fredholm and Fredholm spectra of weighted compositions on $C(K)$, case of non-invertible surjections

We characterize lower semi-Fredholm and Fredholm of weighted composition operators on $C(K)$ in the case when the corresponding map is an open surjection of the compact space $K$ onto itself. The obtained criterions involve the notion of almost homeomorphisms of compact spaces.

Unbounded composition operators via inductive limits: cosubnormal operators with matrix symbols. II

The paper deals with unbounded composition operators with infinite matrix symbols acting in $L^2$-spaces with respect to the gaussian measure on $\mathbb{R}^\infty$. We introduce weak cohyponormality classes $\EuScript{S}_{n,r}^*$ of unbounded operators and provide criteria for the aforementioned composition operators to belong to $\EuScript{S}_{n,r}^*$. Our approach is based on inductive limits of operators.

Composition operators on the spaces of Harmonic Bloch functions

In this paper we characterize some basic properties of composition operators on the spaces of harmonic Bloch functions. First we provide some equivalent conditions for boundedness and compactness of composition operators. Then by using these conditions we estimate the essential norm of composition operators. These results extends the similar results that were proven in the literature on the Bloch spaces.

Compact differences of composition operators on weighted Dirichlet spaces

Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces $\mathcal{D}_α$. Specifically we study differences of composition operators on the Dirichlet space $\mathcal{D}$ and $S^2$, the space of analytic functions whose first derivative is in $H^2$, and then use Calderón's complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.

On properties of multiplication and composition operators between Orlicz spaces

In this paper, we study bounded and closed range multiplication and composition operators between two different Orlicz spaces.

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。

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.

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…

On the composition of integral operators acting in tempered Colombeau algebras

We show that the generalised composition of generalised integral operators is well defined on the space Colombeau algebras of tempered generalised functions.

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.

Compact composition operators on the Dirichlet space and capacity of sets of contact points

In this paper, we prove that for every compact set of the unit disk of logarithmic capacity 0, there exists a Schur function both in the disk algebra and in the Dirichlet space such that the associated composition operator is in all Schatten classes (of the Dirichlet space), and for which the set of points whose image touches the unit circle is equal to this compact set. We show that for every bounded composition operator on the Dirichlet space and for every point of the unit circle, the logarithmic capacity of the set of point having this point as image is 0. We show that every compact compos…

Li-Yorke and Expansive Composition Operators on Lorentz Spaces

In this paper, we investigate Li-Yorke composition operators and some of their variations on Lorentz spaces. Further, we also study expansive composition operators on these spaces. The work of the paper is essentially based on the work in [1], [9], [11], and [13].

Complex Symmetry and Normality of Toeplitz Composition Operators on the Hardy space

In this paper, we investigate the conditions under which the Toeplitz Composition operator on the Hardy space $\mathcal{H}^2$ becomes complex symmetric with respect to a certain conjugation. We also study various normality conditions for the Toeplitz Composition operator on $\mathcal{H}^2$.

Complex symmetric composition operators induced by linear fractional transformations

In this paper we give the answers to two open questions on complex symmetric composition operators. By doing this, we give a complete description of complex symmetric composition operators whose symbols are linear fractional.

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

On the properties of Ascent and Descent of Composition operator on Orlicz spaces

Here, the composition operators on Orlicz spaces with finite ascent and descent as well as infinite ascent and descent are characterized.

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 $A(D).$

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.