Results 41 to 50 of about 1,093 (132)

Fast orbital convergence reveals more hypercyclic vectors

Applied General Topology
Let X be an infinite dimensional separable Banach space, T : X → X be a hypercyclic operator, and x ∈ X be a (frequently) hypercyclic vector of T. We show that if the terms from the T-orbit of x converge to a vector y sufficiently fast, then y is also a ...
T. K. Subrahmonian Moothathu
doaj   +1 more source

Algebras of frequently hypercyclic vectors

, 2019
We show that the multiples of the backward shift operator on the spaces $\ell_{p}$, $1\leq ...
Falcó, Javier, Grosse-Erdmann, Karl-G.
core   +1 more source

Common hypercyclic vectors for families of operators [PDF]

, 2008
We provide a criterion for the existence of a residual set of common hypercyclic vectors for an uncountable family of hypercyclic operators which is based on a previous one given by Costakis and Sambarino.
Gallardo-Gutierrez, E.A., Partington, J.R.   +1 more
core   +1 more source

S‐Mixing Tuple of Operators on Banach Spaces

Journal of Function Spaces, Volume 2016, Issue 1, 2016., 2016
We consider the question: what is the appropriate formulation of Godefroy‐Shapiro criterion for tuples of operators? We also introduce a new notion about tuples of operators, S‐mixing, which lies between mixing and weakly mixing. We also obtain a sufficient condition to ensure a tuple of operators to be S‐mixing.
Wei Wang, Yonglu Shu, Xingzhong Wang, Enrique Llorens-Fuster   +3 more
wiley   +1 more source

CHAOTIC AND HYPERCYCLIC OPERATORS ON SOLID BANACH FUNCTION SPACES

Проблемы анализа, 2020
In this paper, we study hypercyclicity on solid Banach function spaces, and give the characterization for weighted translation operators to be hypercyclic in terms of weight and aperiodic functions.
C-C. Chen, S. M. Tabatabaie
doaj   +1 more source

Commutation relations and hypercyclic operators [PDF]

, 2012
In this paper we establish hypercyclicity of continuous linear operators on $H(\mathbb{C})$ that satisfy certain commutation relations.Comment: Published in Archiv der Mathematik, the final publication is available at springerlink ...
Kim, Vitaly E.
core   +1 more source

Hypercyclic Composition Operators

Journal of Vasyl Stefanyk Precarpathian National University, 2015
In this paper we give survey of hypercyclic composition operators. In pacticular,we represent new classes of hypercyclic composition operators on the spaces of analyticfunctions
openaire   +3 more sources

Hypercyclic operators on topological vector spaces

, 2010
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.
Shkarin, Stanislav
core   +1 more source

Chaos for Cosine Operator Functions on Groups

Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014
Let 1 ≤ p < ∞ and G be a locally compact group. We characterize chaotic cosine operator functions, generated by weighted translations on the Lebesgue space Lp(G), in terms of the weight condition. In particular, chaotic cosine operator functions and chaotic weighted translations can only occur simultaneously.
Chung-Chuan Chen, Wei-Shih Du
wiley   +1 more source

An Extension of Hypercyclicity for N‐Linear Operators

Abstract and Applied Analysis, Volume 2014, Issue 1, 2014., 2014
Grosse‐Erdmann and Kim recently introduced the notion of bihypercyclicity for studying the existence of dense orbits under bilinear operators. We propose an alternative notion of orbit for N‐linear operators that is inspired by difference equations. Under this new notion, every separable infinite dimensional Fréchet space supports supercyclic N‐linear ...
Juan Bès, J. Alberto Conejero, Manuel Maestre   +2 more
wiley   +1 more source