Related papers: Dynamics of composition operators on function spac…
We study the linear dynamics of composition operators induced by measurable transformations on finite measure spaces, with particular emphasis on operators induced by odometers. Our first main result shows that, on a finite measure space,…
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…
The local boundedness of classes of operators is analyzed on different subsets directly related to their Fitzpatrick functions and characterizations of the topological vector spaces for which that local boundedness holds is given in terms…
We study the composition of two set-valued functions defined on locally convex topological linear spaces. We assume that these functions map into certain complete lattices of sets that have been used to establish a conjugation theory for…
Here, the composition operators on Orlicz spaces with finite ascent and descent as well as infinite ascent and descent are characterized.
Using an integral formula on a homogeneous Siegel domain, we show a necessary and sufficient condition for composition operators on the weighted Bergman space of a minimal bounded homogeneous domain to be compact. To describe the…
We consider composition operators in the Dirichlet space of the unit disc in the plane. Various criteria on boundedness, compactness and Hilbert-Schmidt class membership are established. Some of these criteria are shown to be optimal.
We characterize the compactness of composition operators; in term of generalized Nevanlinna counting functions, on a large class of Hilbert spaces of analytic functions, which can be viewed between the Bergman and the Dirichlet spaces
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…
Motivated by the existence of cyclic phenomena in which some characteristics are mapped into corresponding ones over more than one phase, we introduce the $r$-cyclic operators with respect to a covering of a metric space and investigate…
A criterion to obtain frequent hypercyclicity for a sequence of convolution operators on the space of entire functions on the complex plane is provided. The criterion involves that the generating functions of the operators do not vanish on…
We study the properties of power-boundedness, Li-Yorke chaos, distributional chaos, absolutely Ces\`aro boundedness and mean Li-Yorke chaos for weighted composition operators on $L^p(\mu)$ spaces and on $C_0(\Omega)$ spaces. We illustrate…
In this paper, we obtain a complete characterization for the compact difference of two composition operators acting on Bergman spaces with weight $\omega=e^{-\eta}$, $\Delta\eta>0$ in terms of the $\eta$-derived pseudodistance of two…
We present the current results in the study of weighted composition operators on weighted Banach spaces of an unbounded, locally finite metric space. Specifically, we determine characterizations of bounded and compact weighted composition…
In this work, we study the composition operators on the little Lipschitz space ${\mathcal L}_0$ of a rooted tree $T$, defined as the subspace of the Lipschitz space ${\mathcal L}$ consisting of the complex-valued functions $f$ on $T$ such…
We study hypercyclicity properties of a family of non-convolution operators defined on spaces of holomorphic functions on $\mathbb{C}^N$. These operators are a composition of a differentiation operator and an affine composition operator,…
We study composition operators on the Schwartz space of rapidly decreasing functions. We prove that such a composition operator is never a compact operator and we obtain necessary or sufficient conditions for the range of the composition…
In this work we consider refined geometric characterizations of mappings generate composition operators on Sobolev spaces. The detailed proofs in the cases $n-1<q<n$ and $n>q$ are given.
Let $X=(X,\mathcal{B},\mu)$ be a $\sigma$-finite measure space and \mbox{$f:X\to X$} be a measurable transformation such that the composition operator $T_f:\varphi\mapsto \varphi\circ f$ is a bounded linear operator acting on…
We present a general and natural framework to study the dynamics of composition operators on spaces of measurable functions, in which we then reconsider the characterizations for hypercyclic and mixing composition operators obtained by…