Related papers: Hypercyclic Sequences of weighted translations on …
In this paper we are concerned with weighted conditional type(WCT) operators on Orlicz spaces. We prove that all WCT operators have finite ascent. Also, we provide some sufficient conditions for WCT operators to have finite descent. As a…
We prove the existence of common hypercyclic, entire functions for certain families of translation operators.
Let $X$ be a complex topological vector space with dim$(X)>1$ and $\mathcal{B}(X)$ the space of all continuous linear operators on $X$. In this paper, we extend the concept of supercyclicity of a single operators and strongly continuous…
We study the dynamical behaviour of weighted backward shift operators defined on sequence spaces over a directed tree. We provide a characterization of chaos on very general Fr\'echet sequence spaces in terms of the existence of a large…
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…
Given a locally compact group $G$ and $1\leq p<\infty$, a sufficient condition ensuring the \emph{disjoint hypercyclicity} of finitely many weighted translations on $L^p(G)$ was investigated in this paper.
In this paper we establish hypercyclicity of continuous linear operators on $H(\mathbb{C})$ that satisfy certain commutation relations.
We describe a class of topological vector spaces admitting a mixing uniformly continuous operator group ${T_t}_{t\in\C^n}$ with holomorphic dependence on the parameter $t$. This result covers those existing in the literature. We also…
Let $I$ be a countably infinite index set, and let $X$ be a Banach sequence space over $I.$ In this article, we characterize disjoint hypercyclic and supercyclic weighted pseudo-shift operators on $X$ in terms of the weights, the OP-basis,…
We study topological transitivity/hypercyclicity and topological (weak) mixing for weighted composition operators on locally convex spaces of scalar-valued functions which are defined by local properties. As main application of our general…
We first generalize the results of Le\'on and M\"uller [Studia Math. 175(1) 2006] on hypercyclic subspaces to sequences of operators on Fr\'echet spaces with a continuous norm. Then we study the particular case of iterates of an operator T…
It is not known if the inverse of a frequently hypercyclic bilateral weighted shift on $c_0(\mathbb{Z})$ is again frequently hypercyclic. We show that the corresponding problem for upper frequent hypercyclicity has a positive answer. We…
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…
We study frequent hypercyclicity in the context of strongly continuous semigroups of operators. More precisely, we give a criterion (sufficient condition) for a semigroup to be frequently hypercyclic, whose formulation depends on the Pettis…
Bonet, Frerick, Peris and Wengenroth constructed a hypercyclic operator on the locally convex direct sum of countably many copies of the Banach space $\ell_1$. We extend this result. In particular, we show that there is a hypercyclic…
In this paper, we deal with the construction of holomorphic functions on a simply connected domain satisfying that all its derivatives and antiderivatives under a composition operator have a dense orbit. Such functions will be called Luh…
In this paper, a criterion for a sequence of composition operators defined on the space of holomorphic functions in a complex domain to be frequently hypercyclic is provided. Such criterion improves some already known special cases and, in…
In this paper, for a locally compact commutative hypergroup $K$ and for a pair $(\Phi_1, \Phi_2)$ of Young functions satisfying sequence condition, we give a necessary condition in terms of aperiodic elements of the center of $K,$ for the…
In this paper, we study the linear dynamical properties of shift operators on some classes of Segal algebras. Moreover, we characterize hypercyclic generalized bilateral shift operators on the standard Hilbert module.
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.