Related papers: The Essential Norm of Composition Operator between…
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…
In the present article, composition operators induced by Rational Inner Functions on the bidisc $\mathbb{D}^2$ are studied, acting on the weighted Bergman space $A^2_{\beta}(\mathbb{D}^2).$ We prove that under mild conditions that Rational…
By a theorem of Gordon and Hedenmalm, $\varphi$ generates a bounded composition operator on the Hilbert space $\mathscr{H}^2$ of Dirichlet series $\sum_n b_n n^{-s}$ with square-summable coefficients $b_n$ if and only if $\varphi(s)=c_0…
In this paper, we first characterize the polar decomposition of unbounded weighted composition operator pairs $\textbf{C}_{\phi,\omega}$ in an $L^2$-space. Based on this characterization, we introduce the $\lambda$-spherical mean transform…
Based on a judicious partitioning of the preimage of the pseudohyperbolic disk under the composition symbols, in this article, we show that the boundedness and compactness of the sum of two generalized weighted composition operators with…
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…
Let $1\le p<q\le\infty$ and let $T$ be a subadditive operator acting on $L^p$ and $L^q$. We prove that $T$ is bounded on the Orlicz space $L^\phi$, where $\phi^{-1}(u)=u^{1/p}\rho(u^{1/q-1/p})$ for some concave function $\rho$ and \[…
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.
A bounded linear operator $T$ on a separable complex Hilbert space $H$ is called $C$-normal if there is a conjugation $C$ on $H$ such that $ CT^\ast TC=TT^\ast$. Let $\varphi$ be a linear fractional self-map of $\mathbb{D}$. In this paper,…
Let $\varphi$ be a linear-fractional, non-automorphism self-map of $\mathbb{D}$ that fixes $\zeta \in \mathbb{T}$ and satisfies $\varphi^{\prime}(\zeta) \neq 1$ and consider the composition operator $C_{\varphi}$ acting on the Hardy space…
Given pointed metric spaces $X$ and $Y$, we characterize the basepoint-preserving Lipschitz maps $\phi$ from $Y$ to $X$ inducing an isometric composition operator $C_\phi$ between the Lipschitz spaces $Lip_0(X)$ and $Lip_0(Y)$, whenever $X$…
In this paper, we study the weighted compositon operators on weighted Bergman spaces of bounded symmetric domains. The necessary and sufficient conditions for a weighted composition operator $W_{\phi,\psi}$ to be bounded and compact are…
When $\varphi$ and $\psi$ are linear-fractional self-maps of the unit ball $B_N$ in ${\mathbb C}^N$, $N\geq 1$, we show that the difference $C_{\varphi}-C_{\psi}$ cannot be non-trivially compact on either the Hardy space $H^2(B_N)$ or any…
In this paper, we study the boundedness and compactness of the differences of two weighted composition operators acting from $\alpha$-Bloch space to $\beta$-Bloch space on the open unit disk. This study has a relationship to the topological…
We work with very general Banach spaces of analytic functions in the disk or other domains which satisfy a minimum number of natural axioms. Among the preliminary results, we discuss some implications of the basic axioms and identify all…
We introduce the space $\mathcal{W}^{s,p}(\mathbb{D})$ of analytic functions $u$ on the unit disc such that the radial restrictions $u_{r}(\xi):=u(r\xi)$ satisfy the Gagliardo seminorm-only bound \[…
In this paper, we present the current results in the study of weighted composition operators on the Bloch space of bounded homogeneous domains in $\mathbb{C}^n$ with particular emphasis on the issues of boundedness and compactness. We also…
Conditions for a composition operator on the Hardy space of the disk to have closed range or be similar to an isometry are well known. We provide such conditions for composition operators on the Hardy space of the upper half-plane. We also…
The purpose of this paper is to describe the characterization for the compact difference of two composition operators acting between analytic Besov spaces and the weighted little Bloch type space over the unit disk.
The main purpose of this paper is to discuss Hardy type spaces, Bloch type spaces and the composition operators of complex-valued harmonic functions. We first establish a sharp estimate of the Lipschitz continuity of complex-valued harmonic…