Related papers: Common frequent hypercyclicity

We prove that the space $l^2$ contains a dense set of vectors which are hypercyclic simultaneously for all multiples of the backward shift operator by constants of absolute value greater than 1.

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 extend the concept of average expansivity for operators on Banach spaces to operators on arbitrary locally convex spaces. We obtain complete characterizations of the average expansive weighted shifts on Fr\'echet sequence spaces.…

We prove the existence of common hypercyclic, entire functions for certain uncountable families of traslation type operators with relative large gaps.

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…

Bonet, Frerick, Peris and Wengenroth constructed a hypercyclic operator on the locally convex direct sum of countably many copies of the Banach space $\ell_1$. We extend this result. In particular, we show that there is a hypercyclic…

In this paper, we investigate ${\mathcal F}$-hypercyclicity of linear, not necessarily continuous, operators on Fr\' echet spaces. The notion of lower $(m_{n})$-hypercyclicity seems to be new and not considered elsewhere even for linear…

In this paper, we generalise Hardy's uncertainty principle to vector-valued functions, and hence to operators. The principle for operators can be formulated loosely by saying that the kernel of an operator cannot be localised near the…

We solve a number of questions pertaining to the dynamics of linear operators on Hilbert spaces, sometimes by using Baire category arguments and sometimes by constructing explicit examples. In particular, we prove the following results. - A…

Let $T$ be a positive operator on a complex Banach lattice. It is a long open problem whether the peripheral spectrum $\sigma_{\operatorname{per}}(T)$ of $T$ is always cyclic. We consider several growth conditions on $T$, involving its…

This paper is concerned with universality properties of composition operators $C_f$, where the symbol $f$ is given by a transcendental entire function restricted to parts of its Fatou set. We determine universality of $C_f$ when $f$ is…

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…

Quantum chaotic systems exhibit certain universal statistical properties that closely resemble predictions from random matrix theory (RMT). With respect to observables, it has recently been conjectured that, when truncated to a sufficiently…

We exclude the existence of frequently hypercyclic operators that have a spectrum contained in the closed unit disc and that intersects the unit circle in only finitely many points under certain additional conditions. This extends a result…

Let S be the set of scalings 1, 2,3,4, ... and consider the corresponding set of scaled lattices in the plane. In this paper averaging operators are defined for plaquette functions on a lattice to plaquette functions on a coarser lattice…

While numerous extensions of Banach's fixed point theorem typically offer only sufficient conditions for the existence and uniqueness of a fixed point and the convergence of iterative sequences, this study introduces a generalization…

In this short note, we answer a question of Martin and Sanders [Integr. Equ. Oper. Theory, 85 (2) (2016), 191-220] by showing the existence of disjoint frequently hypercyclic operators which fail to be disjoint weakly mixing and, therefore,…

Motivated by the existence of cyclic phenomena in which some characteristics are mapped into corresponding ones over more than one phase, we introduce the $r$-cyclic operators with respect to a covering of a metric space and investigate…

We extend the classical regularity theorem of elliptic operators to maximally hypoelliptic differential operators. More precisely, given vector fields $X_1,\ldots,X_m$ on a smooth manifold which satisfy H\"ormander's bracket generating…

In this paper, the notion of simultaneous universality is introduced, concerning operators having orbits that simultaneously approximate any given vector. This notion is related to the well known concepts of universality and disjoint…