Results 1 to 10 of about 89 (79)

Algebras of frequently hypercyclic vectors [PDF]

Mathematische Nachrichten, 2020
AbstractWe show that the multiples of the backward shift operator on the spaces , , or c0, when endowed with coordinatewise multiplication, do not possess frequently hypercyclic algebras. More generally, we characterize the existence of algebras of ‐hypercyclic vectors for these operators.
Javier Falco, Karl-G Grosse-Erdmann
exaly   +5 more sources

Remarks on common hypercyclic vectors [PDF]

Journal of Functional Analysis, 2010
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 Fréchet space $X$ and a set $Λ\subseteq \R_+\times\C$ which is not of zero three-dimensional Lebesgue measure, the family $\{aT+bI:(a,b)\inΛ\}$ has no common hypercyclic ...
Stanislav Shkarin
exaly   +8 more sources

Perturbations of hypercyclic vectors

Journal of Mathematical Analysis and Applications, 2002
A bounded linear operator \(T\) on a separable Banach space \(\mathcal B\) is said to be hypercyclic if there is \(x \in \mathcal B\), also called hypercyclic, such that the elements in the orbit \(\{T^ n x\}_{n\geq 0}\) are dense in \(\mathcal B\). Hypercyclicity is one of the strongest forms of cyclicity. \textit{S. Rolewicz} [Stud. Math. 32, 17--22 (
Nathan S Feldman
exaly   +2 more sources

Common hypercyclic vectors for the unitary orbit of a hypercyclic operator

Journal of Mathematical Analysis and Applications, 2012
The authors continue their recent work on common hypercyclic vectors for paths and similarity orbits of operators \(T\) on a separable Hilbert space \(H\) [J. Oper. Theory 61, 191--233 (2009); ibid. 66, No.~1, 107--124 (2011; Zbl 1230.47021); J. Math. Anal. Appl. 375, No.~1, 139--148 (2011; Zbl 1208.47013); Integral Equations Oper.
Kit Chan, Rebecca Sanders
exaly   +3 more sources

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   +4 more sources

Existence of Hypercyclic Operators on Topological Vector Spaces

Journal of Functional Analysis, 1997
The author establishes the following result: Suppose \(X\) is a topological vector space with a bounded biorthogonal system \(\{x_n, f_n\}\). Suppose \(X\) is \(\ell^1\)-complete with respect to \((x_n)\). (a) If \(\widetilde T: X\to X\) is continuous and \(\widetilde T(x_n)= w_nx_{n-1}\) for some bounded sequence \((w_n)\) of positive real numbers ...
exaly   +3 more sources

On linear chaos in function spaces

Demonstratio Mathematica, 2022
We show that, in Lp(0,∞){L}_{p}\left(0,\infty ) (1 ...
Jimenez John M., Markin Marat V.
doaj   +1 more source

Invariant Manifolds of Hypercyclic Vectors [PDF]

Proceedings of the American Mathematical Society, 1993
We show that any hypercyclic operator on Hilbert space has a dense, invariant linear manifold consisting, except for zero, entirely of hypercyclic vectors.
openaire   +2 more sources

Generalized bilateral shifts of higher multiplicity [PDF]

Arab Journal of Mathematical Sciences
PurposeSince weighted shifts play a vital role in linear dynamics so in 2021 Chan & Sanders considered weighted shift operators on ℓp(Z) that are not hypercyclic and proved that under certain conditions they can be factorized as products of hypercyclic ...
Munmun Hazarika, Silpi Sikha Das
doaj   +1 more source

Linear Structure of Hypercyclic Vectors

Journal of Functional Analysis, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
León-Saavedra, Fernando, Montes-Rodrı́guez, Alfonso   +1 more
openaire   +2 more sources