Related papers: Multiplication and composition operators between t…
Let $\varphi$ be a holomorphic map which is a symbol of a bounded composition operator $C_\varphi$ acting on the Hardy-Hilbert space of Dirichlet series. We find a K\"onigs map for $\varphi$. We then deduce several applications on…
In this paper, we investigate the normal weighed composition operators $W_{\psi,\varphi}$ which is $\mathcal{J}-$symmetric, $\mathcal{C}_1-$symmetric and $\mathcal{C}_2-$symmetric on the Hardy space $H^2(\mathbb{D})$ respectively. Firstly,…
We study the hypercyclic, supercyclic and cyclic properties of composition operator $C_{\phi}$ on the Segal-Bargmann space $\mathscr{H}(\mathscr{E})$, where $\phi (z)=Az+b$, $A\in \mathcal{B}(\mathscr{E})$, $b\in \mathscr{E}$ with…
We show that there exist non-compact composition operators in the connected component of the compact ones on the classical Hardy space $H^2$ on the unit disc. This answers a question posed by Shapiro and Sundberg in 1990. We also establish…
In this paper, we characterize supercyclic weighted composition operators on a large class of solid Banach function spaces, in particular on Lebesgue, Orlicz and Morrey spaces. Also, we characterize supercyclic weighted composition…
We establish complete characterizations of various notions of expansivity for weighted composition operators on a very general class of locally convex spaces of continuous functions. This class includes several classical classes of…
We survey recent results about composition operators induced by analytic self-maps of the unit disk in the complex plane on various Banach spaces of analytic functions taking values in infinite-dimensional Banach spaces. We mostly…
By using the Schur test, we give some upper and lower estimates on the norm of a composition operator on $\mathcal{H}^2$, the space of Dirichlet series with square summable coefficients, for the inducing symbol $\varphi(s)=c_1+c_{q}q^{-s}$…
We derive in this preprint the exact up to multiplicative constant non-asymptotical estimates for the norms of some non-linear in general case operators, for example, the so-called maximal functional operators, in two probabilistic…
We study invertibility of bounded composition operators of Sobolev spaces. The problem is closely connected with the theory of mappings of finite distortion. If a homeomorphism $\varphi$ of Euclidean domains $D$ and $D'$ generates by the…
In this paper, we provide a unifying theory concerning the convergence properties of the so-called max-product Kantorovich sampling operators based upon generalized kernels in the setting of Orlicz spaces. The approximation of functions…
H. J. Schwartz proved in his thesis (1969) that a nonzero bounded operator on Hardy spaces $(H^p, 1\leq p\leq\infty)$ is almost multiplicative if and only if it is a composition operator. But, his proof has a gap. In this article, we show…
We determine the boundedness and compactness of a large class of operators, mapping from general Banach spaces of holomorphic functions into a particular type of spaces of functions determined by the growth of the functions, or the growth…
Suppose $\varphi$ is a holomorphic self map of the unit disk and $C_\varphi$ is a composition operator with symbol $\varphi$ that fixes the origin and $0<|\varphi'(0)|<1$. This work explores sufficient conditions that ensure all holomorphic…
We obtain some estimates for norm and essential norm of the difference of two composition operators between weighted Bergman spaces $A^p_\alpha$ and $A^q_\beta$ on the unit ball. In particular, we completely characterize the boundedness and…
We provide complete characterisations of nuclear weighted composition operators between two distinct $L^p(\mu)$-spaces, where $1\leq p<\infty$. As a consequence, when the underlying measure space is non-atomic, the only nuclear weighted…
In this note we give a new sufficient condition for the boundedness of the composition operator on the Dirichlet-type space on the disc, via a two dimensional change of variables formula. With the same formula, we characterise the bounded…
For a Young function $\phi$ and a locally compact second countable group $G,$ let $L^\phi(G)$ denote the Orlicz space on $G.$ In this article, we present a necessary and sufficient condition for the topological transitivity of a sequence of…
We give different types of new characterizations for the boundedness and essential norms of generalized weighted composition operators between Zygmund type spaces. Consequently, we obtain new characterizations for the compactness of such…
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…