Related papers: Symmetries and reflections from composition operat…
A conjugation $C$ on a separable complex Hilbert space $\mathcal H$ is an antilinear operator that is isometric and involutive. In this notes, we characterize all conjugations on the Hardy-Hilbert space $H^{2}$ over the disk. In addition,…
For any analytic self-map $\psi$ of $\{z: |z| < 1\}$, J. H. Shapiro has established that the square of the essential norm of the composition operator $C_\psi$ on the Hardy Space $H^2$ is precisely $\limsup_{|w|\rightarrow…
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 $A^*$.…
We study a semigroup of weighted composition operators on the Hardy space of the disk $H^2(\mathbb{D})$, and more generally on the Hardy space $H^2(U)$ attached to a simply connected domain $U$ with smooth boundary. Motivated by conformal…
We compare the compactness of composition operators on $H^2$ and on Orlicz-Hardy spaces $H^\Psi$. We show in particular that exists an Orlicz function $\Psi$ such that $H^{3+\eps} \subseteq H^\Psi \subseteq H^3$ for every $\eps >0$, and a…
Let $\varphi$ be a self-map of the unit disk and let $C_\varphi$ denote the composition operator acting on the standard Dirichlet space $\mathcal{D}$. A necessary condition for compactness of a difference of two bounded composition…
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…
Let g be an analytic function on the open unit disc U such that g(U) is contained in U, and let h be an analytic function on U such that the weighted composition operator W_{h,g) defined by W_{h,g}f = h f(g) is bounded on the Hardy space…
This paper investigates composition operators and weighted composition operators on semi-Hilbert spaces induced by positive multiplication operators on \( L^2(\mu) \). Within the framework of \( A \)-adjoint operators, we characterize…
We construct an analytic self-map $\Phi$ of the bidisk ${\mathbb D}^2$ whose image touches the distinguished boundary, but whose approximation numbers of the associated composition operator on $H^2 ({\mathbb D}^2)$ are small in the sense…
We study compactness property of composition operator acting from a model space generated by an inner function to the Hardy space.
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,…
This paper gives some simple estimates of the essential norm for the difference of composition operators induced by $\phi$ and $\psi$ acting on bounded function space in the unit polydiscs $U^n$, where $\phi(z)$ and $\psi(z)$be holomorphic…
In this paper, we explore the complex symmetrical characteristics of weighted composition operators $W_{u, v}$ and weighted composition-differentiation operators $W_{u, v, k_1, k_2, \ldots, k_n}$ on the Hardy space $H^2(\mathbb{D}^n)$ over…
We obtain a necessary and sufficient condition for a weighted composition operator to be co-isometric on a general weighted Hardy space of analytic functions in the unit disk whose reproducing kernel has the usual natural form. This turns…
We completely characterize the spectrum of a weighted composition operator $W_{\psi, \varphi}$ on $H^{2}(\mathbb{D})$ when $\varphi$ has Denjoy-Wolff point $a$ with $0<|\varphi '(a)|< 1$, the iterates, $\varphi_{n}$, converge uniformly to…
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…
As continuation of the study of polynomial approximation and composition operators on Dirichlet spaces of unit disk, which has settled a problem posed by Cima in 1976, the present paper aims to consider the case of the unbounded domains,…
By a theorem of Bayart, $\varphi$ generates a bounded composition operator on the Hardy space $\Hp$of Dirichlet series ($1\le p<\infty$) only if $\varphi(s)=c_0 s+\psi(s)$, where $c_0$ is a nonnegative integer and $\psi$ a Dirichlet series…
We study the boundedness of composition operators on the bidisk using reproducing kernels. We show that a composition operator is bounded on the Hardy space of the bidisk if some associated function is a positive kernel. This positivity…