Yong-Xin Gao, Ze-Hua Zhou
In this paper we show that a composition operator $C_φ$ cannot be complex symmetric on Hardy-Hilbert space $H^2(D)$ when $φ$ is an elliptic automorphism of order $3$ and not a rotation. This completes the project of finding all invertible composition operators which are complex symmetric $H^2(D)$.
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We give a complete characterization of the spectrum of composition operators, induced by an automorphism of the open unit disk, acting on a family of Banach spaces of analytic functions that includes the Bloch space and BMOA. We show that for parabolic and hyperbolic automorphisms, the spectrum is the unit circle. For the case of elliptic automorphisms, the spectrum is either the unit circle or a finite cyclic subgroup of the unit circle.
In this paper we investigate the numerical ranges of composition operators whose symbols are elliptic automorphisms of finite orders, on the Hilbert Hardy space $H^2(D)$.
Unbounded composition operators via inductive limits: cosubnormals with matrical symbols
利用归纳技巧证明了具有矩阵符号的$L^2$ -空间中的各种无界复合算子是余次正规的.
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.
Adjoints of composition operators with rational symbol
基于Cowen和Gallardo-Gutiérrez提出的方法，我们得到了作用于Hardy空间$H^{2}$上的有理符号复合算子的伴随的具体公式.我们考虑一些具体的例子，比较我们的公式与以前已知的几个结果。
Unbounded composition operators via inductive limits: cosubnormal operators with matrix symbols. II
本文研究了$L^2$ -空间中关于$\mathbb{R}^\infty$上的高斯测度的具有无穷矩阵符号的无界复合算子。我们引入了无界算子的弱余亚正规类$\EuScript{S}_{n,r}^*$，并给出了上述复合算子属于$\EuScript{S}_{n,r}^*$的判据.我们的方法是基于归纳极限的运营商。
Parabolic Non-Automorphism Induced Toeplitz-Composition C*-Algebras with Piece-wise Quasi-continuous Symbols
本文考虑Hilbert-Hardy空间$H^{2}$上由具有分段拟连续符号的Toeplitz算子和由抛物线性分式非自同构符号模紧算子诱导的复合算子生成的C*-代数$C^{*}(\{C_φ\}\cup\mathcal{T}(PQC(\mathbb{T})))/K(H^{2})$.这个C*-代数是交换的。刻画了它的极大理想空间。我们将所得结果应用于一类复合算子与Toeplitz算子的线性组合的本质谱的确定问题。
Quasiconformal symbols and projected composition operators
本文研究了在加权伯格曼空间上具有准共形符号的投影复合算子的可逆性，探讨了符号在不同区域内的共形性质及加权类别的影响。
Composition operators on the Wiener-Dirichlet algebra
本文研究一类狄利克雷级数代数上的复合算子，它是绝对收敛Taylor级数的Wiener代数的类似，我们称之为Wiener-Dirichlet代数.我们研究的运营商和它的符号的属性之间的连接，特别强调这个运营商的紧凑，自守，或等距字符。我们导致中间研究代数的职能，几个，或可数许多，复变数。
Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is proved that if such an operator is bounded, then its symbol is a polynomial of degree at most 1, i.e., it is an affine mapping. Fock's type model for composition operators with linear symbols is established. As a consequence, explicit formulas for their polar decomposition, Aluthge transform and powers with positive real exponents are provided. The theorem of Car…
We give a new proof of the existence of a surjective symbol whose associated composition operator on H 2 (D) is in all Schatten classes, with the improvement that its approximation numbers can be, in some sense, arbitrarily small. We show, as an application, that, contrary to the 1-dimensional case, for N $\ge$ 2, the behavior of the approximation numbers a n = a n (C $Φ$), or rather of $β$ -- N = lim inf n$\rightarrow$$\infty$ [a n ] 1/n 1/N or $β$ + N = lim sup n$\rightarrow$$\infty$ [a n ] 1/n 1/N , of composition operators on H 2 (D N) cannot be determined by the image of the symbol. MSC 2…
We study the spectrum of operators in the Schwartz space of rapidly decreasing functions which associate each function with its composition with a polynomial. In the case where this operator is mean ergodic we prove that its spectrum reduces to 0, while the spectrum of any non mean ergodic composition operator with a polynomial always contains the closed unit disc except perhaps the origen. We obtain a complete description of the spectrum of the composition operator with a quadratic polynomial or a cubic polynomial with positive leading coefficient.
We study topologizability and power boundedness of weigh\-ted composition operators on (certain subspaces of) $\mathscr{D}'(X)$ for an open subset $X$ of $\mathbb{R}^d$. For the former property we derive a characterization in terms of the symbol and the weight of the weighted composition operator, while for the latter property necessary and sufficient conditions on the weight and the symbol are presented. Moreover, for an unweighted composition operator a characterization of power boundedness in terms of the symbol is derived for the special case of a bijective symbol.
Composition operators on the Wiener-Dirichlet algebra
研究一类狄利克雷级数代数上的复合算子，该代数是绝对收敛Taylor级数的Wiener代数的类似代数，我们称之为Wiener-Dirichlet代数.中心问题是要理解操作符和它的符号的属性之间的联系，特别强调这个操作符的紧凑，自守或等距字符。我们导致中间研究代数的职能，几个，或可数许多，复变数。
Spectra of Composition Operators with Symbols in S(2)
设H^2（D）表示复平面上开单位圆盘D的经典Hardy空间。我们得到了H^2（D）上符号属于Kriete和Moorhouse [Trans.Amer.Math.Soc.，359，2007年]。我们的工作揭示了复合算子谱形状的新的可能性，解决了Cowen [J. Operator Th. 9，1983]。我们的结果依赖于一些引理，也许是独立的利益，提供频谱特征的总和的元素的单位代数在一个领域时，某些成对产品的和项为零。
In this paper, we find complex symmetric composition operators on the classical Hardy space whose symbols are linear-fractional but not automorphic. In doing so, we answer a recent question of Noor, and partially answer the original problem posed by Garcia and Hammond.
Compact composition operators with non-linear symbols on the $H^2$ space of Dirichlet series
研究了由映射$φ(s)=c_0s+φ_0(s)$诱导的狄利克雷级数的Hardy空间上的复合算子的紧性，其中$φ_0$是狄利克雷多项式.我们的研究结果在很大程度上依赖于$φ$的特征$c_0$，当$c_0=0$时，在$φ_0$的程度和它的局部行为附近的边界点。我们还研究了其中一些算子的逼近数。我们的方法涉及Carleson措施和微分几何工具的几何估计。
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.
In the present paper, we study the composition operators acting on weighted Hardy spaces of polynomial growth, which are concerned with norms, spectra and (semi-)Fredholmness. Firstly, we estimate the norms of the composition operators with symbols of disk automorphisms. Secondly, we discuss the spectra of the composition operators with symbols of disk automorphisms. In particular, it is proven of that the spectrum of a composition operator with symbol of any parabolic disk automorphism is always the unit circle. Thirdly, we consider the Fredholmness of the composition operator $C_φ$ with symb…
Slice Regular Composition Operators on Quaternionic Fock Spaces via Matrix Realization
研究四元数Fock空间上Volterra型积分算子与复合算子的乘积，通过Berezin型测试量刻画了其有界性和紧性，并利用矩阵符号的特征值映射给出了等价条件。
Extremal Non-Compactness of Composition Operators with Linear Fractional Symbol
以线性分式符号作为超几何函数的根，实现了Hardy空间上大多数复合算子的范数。这一实现给出了符号表现极值非紧性的简单的充要条件，建立了线性分式符号复合算子的余亚正规性和余次正规性的等价性，并给出了由Hardy空间中的正规再生核上伴随的作用决定范数的线性分式复合算子的完全分类.
In this paper, we study quasinormal and hyponormal composition operators \W with linear fractional compositional symbol $\ph$ on the Hardy and weighted Bergman spaces. We characterize the quasinormal composition operators induced on $H^{2}$ and $A_α^{2}$ by these maps and many such weighted composition operators, showing that they are necessarily normal in all known cases. We eliminate several possibilities for hyponormal weighted composition operators but also give new examples of hyponormal weighted composition operators on $H^2$ which are not quasinormal.
We consider composition operators $\mathscr{C}_φ$ on the Hardy space of Dirichlet series $\mathscr{H}^2$, generated by Dirichlet series symbols $φ$. We prove two different subordination principles for such operators. One concerns affine symbols only, and is based on an arithmetical condition on the coefficients of $φ$. The other concerns general symbols, and is based on a geometrical condition on the boundary values of $φ$. Both principles are strict, in the sense that they characterize the composition operators of maximal norm generated by symbols having given mapping properties. In particula…
Composition operators on weighted Bergman spaces of the polydisc
本文研究了多项式盘上加权伯格曼空间之间的复合算子，证明了连续性的一般结果，并通过三重盘的例子展示了仅依赖导数表征连续性的困难。
In this paper, we introduce a general class of weighted spaces of holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. In the particular case when the symbol inducing the composition operator is an affine function, we give criteria for boundedness and compactness. We also study the cyclicity property and as a byproduct give a sufficient condition so that the direct sum of the identity plus a weighted forward shift operator on the Hardy space H^2 is cyclic.
In this paper we study the dynamics of the composition operators defined in the Schwartz space $\mathcal{S}(\mathbb{R})$ of rapidly decreasing functions. We prove that such an operator is never supercyclic and, for monotonic symbols, it is power bounded only in trivial cases. For a polynomial symbol $φ$ of degree greater than one we show that the operator is mean ergodic if and only if it is power bounded and this is the case when $φ$ has even degree and lacks fixed points. We also discuss the spectrum of composition operators.
Königs maps and commutants of composition operators on the Hardy-Hilbert space of Dirichlet series
本文研究了Dirichlet级数Hardy-Hilbert空间上的有界复合算子，通过构造Königs映射推导出其谱与动力学性质，并探讨了一大类符号下复合算子是否具有极小换子。
This paper seeks to extend the theory of composition operators on analytic functional Hilbert spaces from analytic symbols to quasiconformal ones. The focus is the boundedness but operator-theoretic questions are discussed as well. In particular, we present a thorough analysis of $L^p$-estimates of a class of singular integral operators $P_φ$ associated with a quasiconformal mapping $φ$.
Linear dynamics of composition operators on Schwartz spaces
该研究分析Schwartz空间上复合算子的线性动力学，证明可逆复合算子非广义双曲、符号有不动点时算子无正阴影性质，给出符号使算子正拓扑膨胀的条件，刻画仿射符号并明确奇偶次多项式符号的膨胀性差异。
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.
Composition operators on de Branges spaces of entire functions
研究复合算子从模型空间到上半平面Hardy Hilbert空间的有界性和紧性，探讨de Branges空间上复合算子的有界性和紧性，并指出在正则de Branges空间上复合算子的有界性迫使诱导符号为仿射，反之亦然。
Abstract composition laws and their modulation spaces
对于定义在R^2n上的函数类，我们引入了抽象的合成律，该合成律是以符号的伪微分积为模型的。我们重视这些组成法律调制映射和空间有用的代数和拓扑性质。
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.
C*-algebras generated by multiplication operators and composition operators with rational symbol
设$R$是一个二次以上的有理函数，$J_R$是$R$的Julia集，$μ^L$是$R$的Lyubich测度.研究了$C(J_R)$上所有连续函数的乘法算子生成的C-$^*$ -代数$\mathcal{MC}_R$和$L^2(J_R, μ^L)$上由$R$诱导的复合算子$C_R$.证明了复动力系统$\{R^{\circ n} \}_{n=1} ^\infty$的C-$^*$-代数$\mathcal{MC}_R$与C-$^*$-代数$\mathcal{O}_R (J_R)$同构.
Estimates for approximation numbers of some classes of composition operators on the Hardy space
我们给出了复合算子在$H^2$上的逼近数的估计。对于图像包含在多边形中的符号，我们得到这些近似数受$\e^{- c \sqrt n}$支配。当符号在封闭单位圆盘上是连续的，并且在有限个点处有一个非切向接触边界的域，并且在这些点周围的边界处具有良好的行为时，我们可以改进这个上估计。当该符号在某一点具有良好的径向行为时，给出较低的估计。作为一个应用，我们得到了对尖点映射，逼近数等价于$\e^{- c \, n / \log n}$，直到常数，非常接近极小值$\e^{- c \, n}$ .我们也看到了我们方法的局限性。最后，改进了O. El-Fallah，K. Kellay，M. Shabankhah和H. Youssfi，在表明，对于每一个紧凑的集合$K$的单位圆$\T$与勒贝格测度0，存在一个紧凑的组成运营商$C_ϕ\colon H^2 \to H^2$，这是在所有Schatten类，并使$ϕ= 1$对$K$和$|ϕ| < 1$外$K$。
Composition operators on weighted modulation spaces
本文研究了在加权调和空间上由恒等变换扰动构成的复合算子，探讨了 tempered 分布与超分布之间的调和空间作用
In this paper we provide a full characterization of cyclic composition operators defined on the d-dimensional Fock space $\mathcal F(\mathbb C^d)$ in terms of their symbol. Also, we study the supercyclicity and convex-cyclicity of this type of operators. We end this work by computing the approximation numbers of compact composition operators defined on $\mathcal F(\mathbb C^d)$.
Given a symbol $φ,$ i.e., a holomorphic endomorphism of the unit disc, we consider the composition operator $C_φ(f)=f\circφ$ defined on the Banach spaces of holomorphic functions $A(\mathbb{D})$ and $H^{\infty}(\mathbb{D})$. We obtain different conditions on the symbol $φ$ which characterize when the composition operator is mean ergodic and uniformly mean ergodic in the corresponding spaces. These conditions are related to the asymptotic behaviour of the iterates of the symbol. As an appendix, we deal with some particular case in the setting of weighted Banach spaces of holomorphic functions.
The aim of this paper is to study when two composition operators on the Hilbert space of Dirichlet series with square summable coefficients belong to the same component or when their difference is compact. As a corollary we show that if a linear combination of composition operators with polynomial symbols of degree at most 2 is compact, then each composition operator is compact.
Composition operators on the Hardy space of the tridisc
本文研究三圆盘Hardy空间上的复合算子，利用符号映射在边界点处一、二阶导数的行为给出其有界性的充要条件，并进一步讨论二圆盘与三圆盘情形下的紧性。
In this paper, we study the basic properties such as boundedness and compactness of composition operators on discrete analogue of generalized Hardy space defined on a homogeneous rooted tree. Also, we compute the operator norm of composition operator when inducing symbol is automorphism of a homogenous tree.
We give sufficient conditions on the Lebesgue exponents for compositions of odd numbers of pseudo-differential operators with symbols in modulation spaces. As a byproduct, we obtain sufficient conditions for twisted convolutions of odd numbers of factors to be bounded on Wiener amalgam spaces.
The main problem considered in this article is the following: if $\mathbf{F}$, $\mathbf{E}$ are normed spaces of continuous functions over topological spaces $X$ and $Y$ respectively, and $ω:Y\to\mathbb{C}$ and $Φ:Y\to X$ are such that the weighted composition operator $W_{Φ,ω}$ is continuous, when can we guarantee that both $Φ$ and $ω$ are continuous? An analogous problem is also considered in the context of spaces of holomorphic functions over (connected) complex manifolds. Additionally, we consider the most basic properties of the weighted composition operators, which only have been proven …
On approximation numbers of composition operators
我们证明了单位圆的加权Bergman空间$\mathfrak{B}_α$上的紧致复合算子的逼近数可以任意缓慢地趋于0，但它们永远不会迅速趋于0：它们至少呈指数增长，并且这种收敛速度只适用于不接近单位圆的符号。我们还给出了一个上界和一个显式例子。
Composition operators for holomorphic Lipschitz functions
本文研究了在复Banach空间的开单位球上全纯Lipschitz函数空间上的复合算子，通过全纯Lipschitz自由空间线性化符号，将复合算子表示为线性算子的伴随。对于具有有界近似性质的空间，研究了复合算子在全纯Lipschitz函数空间上的性质，并探讨了其紧性和弱紧性，最后分析了复合算子迭代的渐进行为。
Schatten class composition operators on the Hardy space of Dirichlet series and a comparison-type principle
本文刻画了Dirichlet级数Hardy空间上复合算子属于Schatten类的充要条件，建立了比较型原理，并证明多边形紧性定理的类似结果。
Composition operators between Toeplitz kernels
本文研究Toeplitz核在内函数复合算子下的像，确定包含该像的最小Toeplitz核，推广至加权情形，并给出最小模型空间对应结果及显式极大向量。
Dynamics of composition operators on spaces of holomorphic functions on plane domains
本文刻画了平面域上全纯函数空间中加权复合算子的超循环性与拓扑混合性之间的等价关系，并针对穿孔平面、穿孔圆盘及有限连通域等情形给出了超循环性的完整判据。
Weighted symbol spaces, magnetic translations, and pseudodifferential operators
该研究聚焦J. Sjöstrand提出的微局部有限正则性赋范符号空间相关伪微分算子，证明其在调制空间的有界性与Weyl合成积的连续性。
For holomorphic pairs of symbols $(u, ψ)$, we study various structures of the weighted composition operator $ W_{(u,ψ)} f= u \cdot f(ψ)$ defined on the Fock spaces $\mathcal{F}_p$. We have identified operators $W_{(u,ψ)}$ that have power bounded and uniformly mean ergodic properties on the spaces. These properties are described in terms of easy to apply conditions relying on the values $|u(0)|$ and $|u(\frac{b}{1-a})|$ where $ a$ and $b$ are coefficients from linear expansion of the symbol $ψ$. The spectrum of the operators are also determined and applied further to prove results about uniform…
We observe that local embedding problems for certain Hardy and Bergman spaces of Dirichlet series are equivalent to boundedness of a class of composition operators. Following this, we perform a careful study of such composition operators generated by polynomial symbols $φ$ on a scale of Bergman--type Hilbert spaces $\mathcal{D}_α$. We investigate the optimal $β$ such that the composition operator $\mathcal{C}_φ$ maps $\mathcal{D}_α$ boundedly into $\mathcal{D}_β$. We also prove a new embedding theorem for the non-Hilbertian Hardy space $\mathcal H^p$ into a Bergman space in the half-plane and …
Spectra of some composition operators and associated weighted composition operators
刻画了作用在开单位圆盘U的Hardy空间H-2上的“本质线性分式”复合算子的谱和本质谱。当这些复合算子的符号在单位圆上具有Denjoy-Wolff点时，谱与本质谱重合。我们的工作使我们能够描述谱和本质谱的某些相关的加权复合算子的Hardy空间。
Multivalued linear operators, also known as linear relations, are studied on a specific class of weighted, composition transforms on Fock space. Basic properties of this class of linear relations, such as closed graph, boundedness, complex symmetry, real symmetry, or isometry are characterized in simple algebraic terms, involving their symbols.
Symbolic calculus and Fredholm property for localization operators
我们研究的时间fffflessly本地化运营商（波包运营商）的组成，并开发了一个符号演算调制空间上这样的运营商。时间-频率方法（相空间方法）的使用允许使用超快速增长的粗糙符号来代替标准类中的平滑符号。作为主要的应用，它表明，在一般情况下，局部化算子具有Fredholm性质，因此它的范围是封闭的目标空间。
Interactions between Universal Composition Operators and Complex Dynamics
本文研究由超越整函数限制在 Fatou 集部分区域上诱导的复合算子的通用性，刻画了 Baker 域和游荡域上的通用性及通用向量在周期点与无穷远附近的行为，并建立加权复合算子的主通用性定理，进而推广到各类 Fatou 分量。
Contact points and Schatten composition operators
研究了Schatten类Hardy空间和Dirichlet空间上的复合算子。我们给出了一些新的例子，并分析了这类算子的符号的切集的大小。
We study the cyclic and supercyclic dynamical properties of weighted composition operators on the Fock space $\mathcal{F}_2$. A complete characterization of cyclicity which depends on the derivative of the symbol for the composition operator and zeros of the weight function is provided. It is further shown that the space fails to support supercyclic weighted composition operators. As a consequence, we also noticed that the space supports no cyclic multiplication operator.
We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of complex quadratic forms, from the point of view of Fourier integral operators in the complex domain. Sufficient conditions are established for the composition of two such operators to be a Toeplitz operator.
Operators commuting with complex symmetric weighted composition operators on $H^2$
本文研究 Hardy 空间上加权复合算子与复对称加权复合算子的交换性，给出符号条件，并依据符号不动点证明其正规性与复对称性。
In this paper, we study 2-complex symmetric composition operators with the conjugation $J$ on the Hardy space $H^2$. More precisely, we obtain the necessary and sufficient condition for the composition operator $C_ϕ$ to be 2-complex symmetric when the symbols $ϕ$ is an automorphism of $\mathbb D$. We also characterize the 2-complex symmetric composition operator $C_ϕ$ on the Hardy space $H^2$ when $ϕ$ is a linear fractional self-map of $\mathbb D$.
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