Related papers: A hypercyclicity criterion for non-metrizable topo…

A weighted composition operator on the space of scalar-valued smooth functions on an open set of d-dimensional Euclidean space is supercyclic if and only if it is weakly mixing, and it is strongly supercyclic if and only if it is mixing.…

A radially weighted Besov space $H$ is a space of holomorphic functions on the unit ball $\mathbb{B}_d \subseteq \mathbb{C}^d$ whose $N$-th radial derivative is square integrable with respect to a given admissible radial measure. We write…

In this paper we characterize mixing composition operators acting on the space $\mathscr{O}_M(\mathbb{R})$ of slowly increasing smooth functions. Moreover we relate the mixing property of those operators with the solvability of Abel's…

In this paper, we study the hypercyclic composition operators on weighted Banach spaces of functions defined on discrete metric spaces. We show that the only such composition operators act on the "little" spaces. We characterize the bounded…

In this paper we use Nachbin's holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fr\'echet spaces of entire functions of bounded type of infinitely many complex variables.

Given a Furstenberg family F and a subset {\Gamma} of C, we introduce and explore the notions of F_{\Gamma}-hypercyclic operator and F-hypercyclic scalar set. First, the study of F_C-hypercyclic operators yields new interesting information…

Let $H(\mathbb{C})$ be the set of all entire functions endowed with the topology of uniform convergence on compact sets. Let $\lambda,b\in\mathbb{C}$, let $C_{\lambda,b}:H(\mathbb{C})\to H(\mathbb{C})$ be the composition operator…

Chan and Seceleanu have shown that if a weighted shift operator on $\ell^p(\mathbb{Z})$, $1\leq p<\infty$, admits an orbit with a non-zero limit point then it is hypercyclic. We present a new proof of this result that allows to extend it to…

Let $X$ be a Banach space with $\dim X>1$ such that $X^{\ast}$, its dual, is separable and $\mathcal{B}(X)$ the algebra of bounded linear operators on $X$. In this paper, we study the passage of property of being supercyclic from an…

In this note we discuss an open problem whether a truncated Toeplitz operator on a model space can be hypercyclic. We compute point spectrum and eigenfunctions for a class of truncated Toeplitz operators with polynomial analytic and…

Let $(T\_\lambda)\_{\lambda\in\Lambda}$ be a family of operators acting on a $F$-space $X$, where the parameter space $\Lambda$ is a subset of $\mathbb R^d$. We give sufficient conditions on the family to yield the existence of a vector…

This paper is devoted to the study of typical properties (in the Baire Category sense) of certain classes of continuous linear operators acting on Fr\'echet algebras, endowed with the topology of pointwise convergence. Our main results show…

We say that a (countably dimensional) topological vector space $X$ is orbital if there is $T\in L(X)$ and a vector $x\in X$ such that $X$ is the linear span of the orbit ${T^nx:n=0,1,...}$. We say that $X$ is strongly orbital if,…

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…

In this work we shall prove new results on the theory of convolution operators on spaces of entire functions. The focus is on hypercyclicity results for convolution operators on spaces of entire functions of a given type and order; and…

In this paper, we study the cyclicity of the shift operator $S$ acting on a Banach space $\X$ of analytic functions on the open unit disc $\D$. We develop a general framework where a method based on a corona theorem can be used to show that…

This paper is devoted to the study of the dynamics of Toeplitz operators $T_F$ with smooth symbols $F$ on the Hardy spaces of the unit disk $H^p$, $p>1$. Building on a model theory for Toeplitz operators on $H^2$ developed by Yakubovich in…

We study hypercyclicity, Devaney chaos, topological mixing properties and strong mixing in the measure-theoretic sense for operators on topological vector spaces with invariant sets. More precisely, our purpose is to establish links between…

In this paper, we study frequent hypercyclicity for strongly continuous semigroups of operators $\left\{T_{t}\right\}_{t\in\Delta}$ indexed with complex sectors. We propose a revised and more natural definition of frequent hypercyclicity…

Let X,Y be two separable Banach or Frechet spaces , and (Tn) , n=1,2,... be a sequence from linear and continuous operators from X to Y . We say that the sequence (Tn) , n=1,2,... is universal , if there exists some vector v in X such that…