Related papers: Composition operators on vector-valued analytic fu…
We obtain criteria for the boundedness and compactness of weighted composition operators between different Fock spaces in $\mathbb{C}^n$. We also give estimates for essential norm of these operators.
Let $\varphi$ be a linear fractional self-map of the open unit disk $\mathbb{D}$ and $H^2$ the Hardy space of analytic functions on $\mathbb{D}$. The goal of this article is to characterize the linear fractional composition operators…
In this paper, we give two new characterizations for the boundedness and compactness of the difference of two weighted composition operators acting from $H^\infty$ to the Bloch space.
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.
We study composition operators of characteristic zero on weighted Hilbert spaces of Dirichlet series. For this purpose we demonstrate the existence of weighted mean counting functions associated with the Dirichlet series symbol, and provide…
We study the notion of recurrence and some of its variations for linear operators acting on Banach spaces. We characterize recurrence for several classes of linear operators such as weighted shifts, composition operators and multiplication…
We show that some previous results concerning the boundedness of differentiation and integration operators on weighted spaces given by radial weights in the unit disk or the complex plane might fail without some natural additional…
We give a necessary and sufficient condition for a holomorphic self-map $\phi$ of the tridisc to induce a bounded composition operator on the associated Hardy space. This condition depends on the behaviour of the first and the second…
We present important characterizations of the Weighted Composition Operator over the Mittag Leffler space of entire functions. These characterizations include the Hilbert-Schmidt and Unitary char-acterizations of the Weighted Composition…
This paper is based on three hours of lectures given by the first author in the "Focus Program on Analytic Function Spaces and their Applications" July 1 -- December 31, 2021, organized by the Fields Institute for Research in Mathematical…
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…
We first obtain a simpler proof of the main results in [IEOT, {\bf 93}(2021), 17], which characterized the bounded and compact differences $C_{u,\varphi}-C_{v,\psi}$ of two weighted composition operators acting from…
It is well known that on the Hardy space $H^2(\mathbb{D})$ or weighted Bergman space $A^2_{\alpha}(\mathbb{D})$ over the unit disk, the adjoint of a linear fractional composition operator equals the product of a composition operator and two…
The behavior of certain weighted Hardy-type operators on rearrangement-invariant function spaces is thoroughly studied with emphasis being put on the optimality of the obtained results. First, the optimal rearrangement-invariant function…
In this paper, we provide some sufficient conditions for the compactness of weighted composition operators on Dirichlet space. Furthermore, we characterize the numerical range of certain classes of weighted composition operators on…
Fix a metric space $M$ and let $\mathrm{Lip}_0(M)$ be the Banach space of complex-valued Lipschitz functions defined on $M$. A weighted composition operator on $\mathrm{Lip}_0(M)$ is an operator of the kind $wC_f : g \mapsto w \cdot g \circ…
We first characterize those composition operators that are essentially normal on the weighted Bergman space $A^2_s(D)$ for any real $s>-1$, where induced symbols are automorphisms of the unit disk $D$. Using the same technique, we…
Motivated by the construction of the free Banach lattice generated by a Banach space, we introduce and study several vector and Banach lattices of positively homogeneous functions defined on the dual of a Banach space $E$. The relations…
Let $C_\varphi$ be a composition operator acting on the Hardy space of the unit disc $H^p$ ($1\leq p < \infty$), which is embedded in a $C_0$-semigroup of composition operators $\mathcal{T}=(C_{\varphi_t})_{t\geq 0}.$ We investigate whether…
In this paper, we investigate the spectra of invertible weighted composition operators with automorphism symbols, on Hardy space $H^2(\mathbb{B}_N)$ and weighted Bergman spaces $A_\alpha^2(\mathbb{B}_N)$, where $\mathbb{B}_N$ is the unit…