Related papers: Disjoint and Simultaneously Hypercyclic Pseudo-Shi…
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 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…
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 give a sufficient condition for two operators to be disjointly frequently hypercyclic. We apply this criterion to composition operators acting on $H(\mathbb D)$ or on the Hardy space $H^2(\mathbb D)$. We simplify a result on disjoint…
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…
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…
Given a unilateral shift $B_w$ (determined by a bounded sequence $w$), a sequence $x \in \ell^2$ is "hypercyclic" for $w$ iff the forward iterates of $x$ under $B_w$ are dense in $\ell^2$. We show that it is possible to make the set of $x…
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.
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…
In this paper, we investigate the properties of disjoint Ces$\grave{a}$ro-hypercyclic operators. First, the definition of disjoint Ces$\grave{a}$ro-hypercyclic operators is provided, and disjoint Ces$\grave{a}$ro-Hypercyclicity Criterion is…
In this paper, based on the work of Vijay K. Srivastava and Harish Chandra, we give a characterization of the unbounded hypercyclic weighted pseudo-shift operator $wC_{\varphi}$ on $\ell^p$ or $c_0$. Moreover we use the hypercyclicity…
We characterize disjoint hypercyclic sequences of wedge operators. Also, we give some sufficient conditions for a sequence of the dual wedge operators to be disjoint topologically transitive. Finally, we give some concrete examples and…
Our aim in this paper is to obtain necessary and sufficient conditions for weighted shift operators on the Hilbert spaces $\ell^{2}(\mathbb Z)$ and $\ell^{2}(\mathbb N)$ to be subspace-transitive, consequently, we show that the Herrero…
Recently, two new topological properties for operators acting on a topological vector space were introduced: strong hypercyclicity and hypermixing. We introduce a new property called ultra hypercyclicity and compare it to strong…
In \cite{SH}, A. L. Shields proved a well-known theorem for the similarity of unilateral weighted shift operators. By using the generalization of this theorem for multivariable weighted shifts and the curvature of holomorphic bundles, we…
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…
We give a short proof of the existence of disjoint hypercyclic tuples of operators of any given length on any separable infinite dimensional Frechet space. A similar argument provides disjoint dual hypercyclic tuples of operators of any…
We show that the bilateral backward shift on $\ell^p(\mathbb{Z},\omega)$ that has a projective orbit with a non-zero limit point is supercyclic. This phenomenon holds also for $\Gamma$-supercyclicity, which extends a result obtained for the…
We study common frequently hypercyclic vectors for countable families of weighted backward shifts acting on $\ell_p$ spaces, $1\leq p<\infty$. Using probabilistic techniques, we develop a general existence criterion, complemented by a…
Let $B$ be an unilateral weighted backward shift on $\ell_p$, $1 \leq p < \infty$, that admits a $\mathscr{U}$-frequently hypercyclic subspace. We prove that $B$ admits such a subspace free of frequently hypercyclic vectors. The proof…