Paul S. Bourdon, Joel H. Shapiro
We give an elementary proof of a formula recently obtained by Hammond, Moorhouse, and Robbins for the adjoint of a rationally induced composition operator on the Hardy space H^2. We discuss some variants and implications of this formula, and use it to provide a sufficient condition for a rationally induced composition operator adjoint to be a compact perturbation of a weighted composition operator.
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We characterize the convex-cyclic weighted composition operators $W_{(u,ψ)}$ and their adjoints on the Fock space in terms of the derivative powers of $ ψ$ and the location of the eigenvalues of the operators on the complex plane. Such a description is also equivalent to identifying the operators or their adjoints for which their invariant closed convex sets are all invariant subspaces. We further show that the space supports no supercyclic weighted composition operators with respect to the pointwise convergence topology and hence with the weak and strong topologies and answers a question rais…
In this paper we study the self-adjoint and co-isometry composition and weighted composition operator on $H_E(ζ).$ We also discuss the conditions under which adjoint operator of a composition and weighted composition operator on $H_E(ζ)$ to be some composition and weighted composition operator, respectively.
In this paper we obtain characterizations for adjoint of a composition and weighted composition operator to be composition and weighted composition operator on $F_ψ^2,$ respectively. We study the co-isometry composition and weighted composition operators on $F_ψ^2.$
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.
Building on techniques developed by Cowen and Gallardo-Gutiérrez, we find a concrete formula for the adjoint of a composition operator with rational symbol acting on the Hardy space $H^{2}$. We consider some specific examples, comparing our formula with several results that were previously known.
We generalize the classical notion of adjoint of a linear operator and the Aron-Schottenloher notion of adjoint of a homogeneous polynomial. The general notion is shown to enjoy several properties enjoyed by the classical ones, nevertheless differences between the two theories are detected. The proofs of both positive and negative results are not simple adaptations of the linear cases, actually nonlinear arguments are often required. Applications of the generalized adjoints to Lindström-Schlüchtermann type theorems for composition operators are provided.
Schatten class membership of products of composition operators and their adjoints
本文研究Hardy与Bergman空间上复合算子及其伴随算子乘积的Schatten类成员性，给出相关算子属于Schatten类的充要条件及特定符号下的充要条件。
Building on techniques used in the case of the disc, we use a variety of methods to develop formulae for the adjoints of composition operators on Hardy spaces of the upper half-plane. In doing so, we prove a slight extension of a known necessary condition for the boundedness of such operators, and use it to provide a complete classification of the bounded composition operators with rational symbol. We then consider some specific examples, comparing our formulae with each other, and with other easily deduced formulae for simple cases.
It is well known that on the Hardy space $H^2(\mathbb{D})$ or weighted Bergman space $A^2_α(\mathbb{D})$ over the unit disk, the adjoint of a linear fractional composition operator equals the product of a composition operator and two Toeplitz operators. On $S^2(\mathbb{D})$, the space of analytic functions on the disk whose first derivatives belong to $H^2(\mathbb{D})$, Heller showed that a similar formula holds modulo the ideal of compact operators. In this paper we investigate what the situation is like on other weighted Hardy spaces.
A pre-adjoint approach on weighted composition operators between spaces of Lipschitz functions
本文利用加权Lipschitz算子这一预伴随视角，重新刻画Lipschitz函数空间间加权复合算子的有界性、紧性及映射性质，并改进已有范数估计。
In this article, we completely characterize the complex symmetry, cyclicity and hypercyclicity of composition operators $C_ϕf=f\circϕ$ induced by affine self-maps $ϕ$ of the right half-plane $\mathbb{C}_+$ on the Hardy-Hilbert space $H^2(\mathbb{C}_+)$. We also provide new proofs for the normal, self-adjoint and unitary cases and for an adjoint formula discovered by Gallardo-Gutiérrez and Montes-Rodrígues.
We realize norms of most composition operators acting on the Hardy space with linear fractional symbol as roots of hypergeometric functions. This realization leads to simple necessary and sufficient conditions on the symbol to exhibit extremal non-compactness, establishes equivalence of cohyponormality and cosubnormality of composition operators with linear fractional symbol, and yields a complete classification of those linear fractional that induce composition operators whose norms are determined by the action of the adjoint on the normalized reproducing kernels in the Hardy space.
Applications of Reproducing Kernels in composition operators
本文通过再现核方法研究复合算子，揭示其在加权 Hardy 空间中的结构特性及分类结果，并简化了若干已知结论的证明过程。
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。
Weighted Composition Operator on Fock Space
研究Fock空间加权复合算子交换与正规条件
We investigate composition-differentiation operators acting on the Dirichlet space of the unit disk. Specifically, we determine characterizations for bounded, compact, and Hilbert-Schmidt composition-differentiation operators. In addition, for particular classes of inducing maps, we derive an adjoint formula, compute the norm, and identify the spectrum.
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.
We investigate composition-differentiation operators acting on the space $S^2$, the space of analytic functions on the open unit disk whose first derivative is in $H^2$. Specifically, we determine characterizations for bounded and compact composition-differentiation operators acting on $S^p$. In addition, for particular classes of inducing maps, we compute the norm, and identify the spectrum. Finally, for particular linear fractional inducing maps, we determine the adjoint of the composition-differentiation operator acting on weighted Bergman spaces which include $S^2, H^2$, and the Dirichlet …
In this paper we deal with unbounded composition operators defined in Orlicz spaces. Indeed, we provide some necessary and sufficient condition for densely definedness of composition operators on Orlicz spaces. Also, we will investigate the adjoint of densely defined composition operators and we give some equivalent conditions for it to be densely defined. In addition, we show that densely defined composition operator is continuous if and only if it is everywhere defined. Finally, we characterize densely defined continuous composition operators.
We determine both the semigroup and spectral properties of a group of weighted composition operators on the Little Bloch space. It turns out that these are strongly continuous groups of invertible isometries on the Bloch space. We then obtain the norm and spectra of the infinitesimal generator as well as the resulting resolvents which are given as integral operators. As consequences, we complete the analysis of the adjoint composition group on the predual on the nonreflexive Bergman space, and a group of isometries associated with a specific automorphism of the upper half plane.
Generalized complex symmetric composition operators with applications
本文刻画了多圆盘和单位圆盘上加权复合-微分算子的复对称性与自伴性条件，研究了广义加权复合微分算子的复对称结构，并探讨了复合算子Berezin值域的凸性及几何解释。
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。
A bounded linear operator $A$ on a Hilbert space is posinormal if there exists a positive operator $P$ such that $AA^{*} = A^{*}PA$. Posinormality of $A$ is equivalent to the inclusion of the range of $A$ in the range of its adjoint $A^*$. Every hyponormal operator is posinormal, as is every invertible operator. We characterize both the posinormal and coposinormal composition operators $C_φ$ on the Hardy space $H^2$ of the open unit disk $\mathbb{D}$ when $φ$ is a linear-fractional selfmap of $\mathbb{D}$. Our work reveals that there are composition operators that are both posinormal and copos…
A Characterization of Complex Symmetric Weighted Composition Operators on the Fock Space
该研究未预先指定共轭算子，借助再生核与生成函数刻画Fock空间上有界复对称加权复合算子，所得共轭算子多为反线性高斯积分算子，部分为加权复合共轭算子。
Composition operators on Hardy-Smirnov spaces
本文研究 Hardy-Smirnov 空间 $H^{2}(Ω)$ 上的复合算子 $C_Φ$，在黎曼映射为线性分式变换时刻画了伴随算子仍为复合算子的条件，并据此重新证明了伴随公式，描述了 Hermitian、酉及复对称复合算子。
We study the relationship between the classical Hamilton flow and the quantum Schrödinger evolution where the Hamiltonian is a degree-2 complex-valued polynomial. When the flow obeys a strict positivity condition equivalent to compactness of the evolution operator, we find geometric expressions for the $L^2$ operator norm and a singular-value decomposition of the Schrödinger evolution, using the Hamilton flow. The flow also gives a geometric composition law for these operators, which correspond to a large class of integral operators with nondegenerate Gaussian kernels.
Dunford property for composition operators on $H^p$-spaces
本文在单位圆盘线性分式变换诱导的复合算子类中完全刻画了$H^p$-空间上复合算子及其伴随算子的Dunford性质$(C)$，并证明该性质在此类中稳定，回答了Laursen和Neumann问题的一个特例。
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。
We study self-adjoint semigroups of partial isometries on a Hilbert space. These semigroups coincide precisely with faithful representations of abstract inverse semigroups. Groups of unitary operators are specialized examples of self-adjoint semigroups of partial isometries. We obtain a general structure result showing that every self-adjoint semigroup of partial isometries consists of "generalized weighted composition" operators on a space of square-integrable Hilbert-space valued functions. If the semigroup is irreducible and contains a compact operator then the underlying measure space is p…
On posinormality of weighted composition-differentiation operators on $H^2(\mathbb{D})$
本文研究了 $H^2(\mathbb{D})$ 上加权复合-微分算子的正则性和共正则性，发现特定选择下加权算子可为正则，推导了其共轭公式并得出了必要条件。
Composition operators on some semi-Hilbert spaces
本文研究半Hilbert空间中复合算子的A-伴随性质，刻画其自伴、正规、拟正规、酉、等距及部分等距的条件，并给出示例验证。
Generalized weighted composition operators on Hardy space $H^2(\mathbb{D}^n)$
本文研究多圆盘Hardy空间上广义加权复合算子的复对称性，给出Hermitian性与正规性的显式条件，并确定算子及其伴随的核。
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。
Composition operators, convexity of their Berezin range and related questions
本文研究再生核 Hilbert 空间中复合算子 Berezin 值域的凸性，刻画 Hardy 与 Bergman 空间情形，并证明正自伴算子在超二次函数下的 Berezin 集映射定理。
Dynamics of operators on the space of Radon measures
本文研究Radon测度空间上加权复合算子伴随算子的动力学，给出其拓扑超传递充要条件与混沌充分条件，还得到带符号Radon测度空间中积分算子伴随诱导的Markov链收敛条件及Radon测度空间的结构结果。
A note on the spectrum of Lipschitz operators and composition operators on Lipschitz spaces
本文研究Lipschitz自由空间上加权Lipschitz算子及其伴随加权复合算子的谱，特别在紧致情形下，证明非加权情形下谱有限且为单位根。
A regular symmetric operator on a Hilbert module is self-adjoint whenever there exists a suitable approximate identity. We say an operator is 'locally bounded' if the composition of the operator with each element in the approximate identity is bounded. We prove that the perturbation of a regular self-adjoint operator by a locally bounded symmetric operator is again regular and self-adjoint. We use this result to show that the Kasparov class represented by an unbounded Kasparov module is stable under locally bounded perturbations. As an application, we show that we obtain a converse to the 'dou…
Generalized weighted composition-differentiation operators on weighted Bergman spaces
本研究在加权Bergman空间$\mathcal{A}^2_α(\mathbb{D})$中探究广义加权复合微分算子$L_{n, ψ, ϕ}$的复对称性，推导其$C_{μ,η}$-对称的充要条件，得到算子为埃尔米特和正规的显式条件，并分析该对称下算子的谱性质与伴随算子的核。
A Projection Characterization and Symmetry Bootstrap for Elements of a von Neumann Algebra that are Nearby Commuting Elements
本文研究 C*-代数中邻近交换算子的对称性提升问题，通过投影刻画证明带对称性的 Lin 定理，并解决拓扑绝缘体相关的一个猜想。
In this paper we develop the calculus of pseudo-differential operators on the lattice $\mathbb{Z}^n$, which we can call pseudo-difference operators. An interesting feature of this calculus is that the phase space is compact so the symbol classes are defined in terms of the behaviour with respect to the lattice variable. We establish formulae for composition, adjoint, transpose, and for parametrix for the elliptic operators. We also give conditions for the $\ell^2$, weighted $\ell^2$, and $\ell^p$ boundedness of operators and for their compactness on $\ell^p$. We describe a link to the toroidal…
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