相关论文: Common hypercyclic vectors for composition operato…
We prove the existence of common hypercyclic, entire functions for certain families of translation operators.
Considering a family of upper frequently hypercyclic operators we care about the existence of vectors which are upper frequently hypercyclic for any operator of this family. We establish sufficient conditions for a family of operators to…
We provide necessary and sufficient conditions on the existence of common hypercyclic vectors for multiples of the backward shift operator along sparse powers. Our main result strongly generalizes corresponding results which concern the…
We prove the existence of algebras of hypercyclic vectors in three cases: convolution operators, composition operators, and backward shift operators.
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…
A criterion and sufficient conditions for a vector to be a cyclic vector for a class of self-adjoint operators are obtained.
We investigate the existence of a common hypercyclic vector for a family $(T_\lambda)_{\lambda\in \Lambda}$ of hypercyclicoperators acting on the same Banach space $X$. We give positive and negative results involving the dimension of…
We prove the existence of common hypercyclic, entire functions for certain uncountable families of traslation type operators with relative large gaps.
Let $(T\_\lambda)\_{\lambda\in\Lambda}$ be a family of operators acting on a $F$-space $X$, where the parameter space $\Lambda$ is a subset of $\mathbb R^d$. We give sufficient conditions on the family to yield the existence of a vector…
We provide with criteria for a family of sequences of operators to share a frequently universal vector. These criteria are variants of the classical Frequent Hypercyclicity Criterion and of a recent criterion due to Grivaux, Matheron and…
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…
We provide criteria for the existence of upper frequently hypercyclic subspaces and for common hypercyclic subspaces, which include the following consequences. There exist frequently hypercyclic operators with upper-frequently hypercyclic…
Recent work by several authors has revealed the existence of many unexpected classes of normal weighted composition operators. On the other hand, it is known that every normal operator is a complex symmetric operator. We therefore undertake…
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 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…
We prove the existence of common hypercyclic entire functions for uncountable families of translation type operators. Contrary to our previous work [34], here the parameter which reflects the uncountable family lies on the unit circle. On…
We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.
We treat the question of existence of common hypercyclic vectors for families of continuous linear operators. It is shown that for any continuous linear operator $T$ on a complex Fr\'echet space $X$ and a set $\Lambda\subseteq \R_+\times\C$…
We study the existence of hypercyclic algebras for convolution operators $\Phi(D)$ on the space of entire functions whose symbol $\Phi$ has unimodular constant term. In particular, we provide new eigenvalue criteria for the existence of…
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…