Related papers: Unbounded Chaotic Weighted Pseudo-shift

Bayart and Ruzsa [Ergodic Theory Dynam. Systems 35 (2015)] have recently shown that every frequently hypercyclic weighted shift on $\ell^p$ is chaotic. This contrasts with an earlier result of Bayart and Grivaux [Proc. London Math. Soc. (3)…

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 characterize disjoint and simultaneously hypercyclic tuples of unilateral pseudo-shift operators on $\ell^p(\mathbb{N})$. As a consequence, complementing the results of Bernal and Jung, we give a characterization for simultaneously…

We show that, in $L_{p}(0,\infty)$ ($1\leq p <\infty$), bounded weighted translations as well as their unbounded counterparts are chaotic linear operators. We also extend the unbounded case to $C_{0}[0,\infty)$ and describe the spectra of…

We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on $\ell^p(\mathbb Z)$, $p\geq 1$. Our method uses properties of the difference set of a set with positive upper…

We analyze the hypercyclicity, chaoticity, and spectral structure of (bounded and unbounded) weighted backward shifts in a nonclassical sequence space, which the space $l_1$ of summable sequences is both isometrically isomorphic to and…

This article is intended to outline some the recent work by the author on the chaoticity of some specific bakward shift unbounded operators realized as differential operators acting on some Fock-Bargmann spaces and give suficient conditions…

We obtain a Disjoint Frequent Hypercyclicity Criterion and show that it characterizes disjoint frequent hypercyclicity for a family of unilateral pseudo-shifts on $c_0(\mathbb{N})$ and $\ell^p(\mathbb{N})$, $1\le p <\infty$. As an…

In this paper, we investigate the distributional chaos of the composition operator $T_{\varphi}:f\mapsto f\circ\varphi$ on $L^{p}(X,\mathcal{B},\mu)$, $1\leq p <\infty$. We provide a characterization and practical sufficient conditions on…

The notions of chaos and frequent hypercyclicity enjoy an intimate relationship in linear dynamics. Indeed, after a series of partial results, it was shown by Bayart and Rusza in 2015 that for backward weighted shifts on…

This article aims to initiate a study of bilateral weighted backward shift operators defined on the spaces $\ell^p_{a,b}(\Omega_{r,R})$ and $c_{0,a,b}(\Omega_{r,R})$ which are Banach spaces of analytic functions on a suitable annulus in the…

Extending previous results of Bourdon and Shapiro we characterize the hypercyclic and mixing composition operators $C_{\varphi}$ for the automorphisms of $\mathbb{D}$ on any of the spaces $H^{p}$ with $1\leqslant p<+\infty$.

We establish complete characterizations of the notion of Li-Yorke chaos for weighted composition operators on $C_0(X)$ spaces and on $L^p(\mu)$ spaces. As a consequence, we obtain simple characterizations of the Li-Yorke chaotic weighted…

we study the hypercyclic and chaotic properties of the time varying weighted backward shift operator $(Tx)(t)=w(t)x(t+a)$ in $L_p(0,\infty)(1\leq p<\infty)$ and $C_0[0,\infty)$. And we also analyse the spectral structure of the operators if…

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…

A conditional weighted composition operator $T_u: L^p(\Sigma)\rightarrow L^p(\mathcal{A})$ ($1\leq p<\infty$), is defined by $T_u(f):= E^{\mathcal{A}}(u f\circ \varphi)$, where $\varphi: X\rightarrow X$ is a measurable transformation, $u$…

We study Li--Yorke and mean Li--Yorke chaos for weighted composition operators $C_{w,\varphi}$ on Banach spaces of analytic functions on the unit disk $\mathbb{D}$. Under natural conditions on the space, we show that $C_{w,\varphi}$ is…

In this paper we consider unbounded weighted conditional type operators on the space Lp, we give some conditions under which they are densely defined and we obtain a dense subset of the domain. Also, we get that a WCT operator is continuous…

We prove the chaoticity and describe the spectral structure of Rolewicz-type weighted backward shift unbounded linear operators in the sequence spaces $l_p$ ($1\le p<\infty$) and $c_0$.

We generalize a result for the translation $C_0$-semigroup on $L^p(\R_+,\mu)$ about the equivalence of being chaotic and satisfying the Frequent Hypercyclicity criterion due to Mangino and Peris to certain weighted composition…