Related papers: Disjoint hypercyclicity of weighted translations

Let $G$ be a locally compact group, and let $1\le p < \infty$. Consider the weighted $L^p$-space $L^p(G,\omega)=\{f:\int|f\omega|^p<\infty\}$, where $\omega:G\to \mathbb R$ is a positive measurable function. Under appropriate conditions on…

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…

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…

A bounded linear operator $T$ on a Banach space $X$ (not necessarily separable) is said to be $J$-class operator whenever the extended limit set, say $J_T(x)$ equals $X$ for some vector $x\in X$. Practically, the extended limit sets…

Frequent hypercyclicity for translation $C_0$-semigroups on weighted spaces of continuous functions is investigated. The results are achieved by establishing an analogy between frequent hypercyclicity for the translation semigroup and for…

We first give a note on disjoint hypercyclicity for invertible bilateral pseudo-shifts on $\ell^{p}(\mathbb{Z})$, $1\leq p <\infty$. It is already known that if a tuple of bilateral weighted shifts on $\ell^{p}(\mathbb{Z})$, $1\leq p…

We give several equivalent characterization of aperiodicity of an element on locally compact group $G$, and give an intuition for "How strong does the aperiodicity of an element affect the existence of hypercyclic weighted translation…

Let $\omega$ be a weight function defined on a locally compact group $G$, $1\le p<+\infty$, $S\subset G$ and let us assume that for any $s\in S$, the left translation operator $T_s$ is continuous from the weighted $L^p$-space…

Let $G$ be a locally compact group, and let $\Phi$ be a Young function. In this paper, we give sufficient and necessary conditions for weighted translation operators on the Orlicz space $L^\Phi(G)$ to be chaotic and topologically multiply…

In this paper, we characterize hypercyclic sequences of weighted translation operators on an Orlicz space in the context of locally compact hypergroups.

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…

A bounded linear operator $T$ on a Banach space $X$ is called a convex-cyclic operator if there exists a vector $x \in X$ such that the convex hull of $Orb(T, x)$ is dense in $X$. In this paper, for given an aperiodic element $g$ in a…

It is shown that for a bounded weighted bilateral shift $T$ acting on $\ell_p(\Z)$ for $1\leq p\leq 2$ supercyclicity of $T$, weak supercyclicity of $T$, cyclicity of $T\oplus T$ and cyclicity of $T^2$ are equivalent. A new sufficient…

Let $G$ be a locally compact group and $1\leq p<\infty$. Based on some important earlier works, in this paper the concept of $L_p^T-$function is introduced. Then the structure of the space $L^{T}_p(G)$, which is consisting of all…

Our paper begins with a revision of spectral theory for commutative Banach algebras, which enables us to prove the $L^p_{\omega}-$conjecture for locally compact abelian groups. We follow an alternative approach to the one known in the…

We analyze $f$-frequently hypercyclic, $q$-frequently hypercyclic ($q> 1$) and frequently hypercyclic $C_{0}$-semigroups ($q=1$) defined on complex sectors, working in the setting of separable infinite-dimensional Fr\'echet spaces. Some…

In this paper, we prove that if a finite disjoint union of translates $\bigcup_{k=1}^n\{f_k(x-\gamma)\}_{\gamma\in\Gamma_k}$ in $L^p(\R^d)$ $(1<p<\infty)$ is a $p'$-Bessel sequence for some $1<p'<\infty$, then the disjoint union…

In this paper we prove that translation structures for which the corresponding vertical translation flows is weakly mixing and disjoint with its inverse, form a $G_\delta$-dense set in every non-hyperelliptic connected component of the…

The flow in a fixed direction on a translation surface S determines a decomposition of S into closed invariant sets, each of which is either periodic or minimal. We study this decomposition for translation surfaces in the hyperelliptic…

We consider the set of H\"older continuous cocycles over a finite shift acting on a group of Lipschitz homeomorphisms Lip(G), where G is a metrisable compact topological group. We establish that two dominated cocycles that coincide over…