Related papers: Hereditarily frequently hypercyclic operators and …
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…
When the backward shift operator on a weighted space $H^2_w=\{f=\sum_{j=0} ^{\infty} a_jz^j : \sum_{j=0}^{\infty} |a_j|^2w_j < \infty\}$ is an $n$-hypercontraction, we prove that the weights must satisfy the inequality $$\frac{w_{j+1}}{w_j}…
In this paper, we generalize to the context of algebras some recent results on the existence of common hypercyclic vectors for families of products of backward shift operators. We also give, in a multi-dimensional setting, a positive answer…
We study hypercyclicity properties of a family of non-convolution operators defined on spaces of holomorphic functions on $\mathbb{C}^N$. These operators are a composition of a differentiation operator and an affine composition operator,…
We give a simple, straightforward proof of the non-hypercyclicity of an arbitrary (bounded or not) normal operator $A$ in a complex Hilbert space as well as of the collection $\left\{e^{tA}\right\}_{t\ge 0}$ of its exponentials, which,…
We prove that a bounded operator $T$ on a separable Banach space $X$ satisfying a strong form of the Frequent Hypercyclicity Criterion (which implies in particular that the operator is universal in the sense of Glasner and Weiss) admits…
A bounded linear operator T on Hilbert space is subspace-hypercyclic for a subspace M if there exists a vector whose orbit under T intersects the subspace in a relatively dense set. We construct examples to show that subspace-hypercyclicity…
A new class of (not necessarily bounded) operators related to (mainly infinite) directed trees is introduced and investigated. Operators in question are to be considered as a generalization of classical weighted shifts, on the one hand, and…
Given a countable dense subset D of an infinite-dimensional separable Hilbert space H the set of operators for which every vector in D except zero is hypercyclic (weakly supercyclic) is residual for the strong (resp. weak) operator topology…
Let $X$ be a complex topological vector space with $dim(X)>1$ and $\mathcal{B}(X)$ the set of all continuous linear operators on $X$. The concept of hypercyclicity for a subset of $\mathcal{B}(X)$, was introduced in \cite{AKH}. In this…
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…
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…
In this paper, we answer a question posed in the introduction of \cite{sub hyp} positively, i.e, we show that if $T$ is $\mathcal M$-hypercyclic operator with $\mathcal M$-hypercyclic vector $x$ in a Hilbert space $\mathcal H$, then…
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…
We establish two Frequent Hypercyclicity Criteria for unbounded operators, inspired by the frameworks of Bayart Grivaux and deLaubenfels Emamirad Grosse Erdmann. These criteria simplify the verification and construction of frequently…
A bounded linear operator $T$ on a Banach space $X$ is called frequently hypercyclic if there exists $x\in X$ such that the lower density of the set $\{n\in\N:T^nx\in U\}$ is positive for any non-empty open subset $U$ of $X$. Bayart and…
In this paper, we introduce a general class of weighted spaces of holomorphic Dirichlet series (with real frequencies) analytic in some half-plane and study composition operators on these spaces. In the particular case when the symbol…
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…
In this paper we initiate the study of a fundamental yet untapped random model of non-selfadjoint, bounded linear operators acting on a separable complex Hilbert space. We replace the weights $w_n=1$ in the classical unilateral shift $T$,…
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…