Results 61 to 70 of about 1,297 (140)

Cyclic Composition operators on Segal-Bargmann space

Concrete Operators, 2022
We study the cyclic, supercyclic and hypercyclic properties of a composition operator Cϕ on the Segal-Bargmann space ℋ(ℰ), where ϕ(z) = Az + b, A is a bounded linear operator on ℰ, b ∈ ℰ with ||A|| ⩽ 1 and A*b belongs to the range of (I – A*A)½ ...
Ramesh G., Ranjan B. Sudip, Naidu D. Venku   +2 more
doaj   +1 more source

Sums of hypercyclic operators

Journal of Functional Analysis, 2003
A (bounded) operator \(T\) on a complex infinite-dimensional separable Banach space \(X\) is said to be hypercyclic if there is a (hypercyclic) vector \(x \in X\) such that its orbit \(O(T,x):=\{x,Tx,T^2x,\dots\}\) is dense in \(X\). The operator \(T\) is called chaotic if it is hypercyclic and the set of periodic points of \(T\) is dense in \(X ...
openaire   +2 more sources

Hypercyclic operators failing the Hypercyclicity Criterion on classical Banach spaces

Journal of Functional Analysis, 2007
Let \(X\) be a topological vector space over \(\mathbb{R}\) or \(\mathbb{C}\). A (continuous, linear) operator \(T:X \to X\) is said to be hypercyclic if there exists some \(x \in X\) whose \(T\)-orbit \(\{T^n x: n\in{\mathbb{N}}\}\) is dense in \(X\). In [J.~Funct.~Anal.\ 99, 179--190 (1991; Zbl 0758.47016)], \textit{D.\,Herrero} posed the problem of ...
Bayart, Frédéric, Matheron, Etienne
openaire   +2 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

Hypercyclic differentiation operators

, 1999
8 ...
Aron, Richard M., Bes, Juan P.
openaire   +2 more sources

Spaces that admit hypercyclic operators with hypercyclic adjoints [PDF]

Proceedings of the American Mathematical Society, 2005
A continuous linear operator T : X → X T:X\to X is hypercyclic if there is an x ∈ X x\in X such that the orbit { T n x } n ≥ 0 \
openaire   +1 more source

$k$-bitransitive and compound operators on Banach spaces

Karpatsʹkì Matematičnì Publìkacìï, 2016
In this this paper, we introduce new classes of operators in complex Banach spaces, which we call $k$-bitransitive operators and compound operators to study the direct sum of diskcyclic operators.
N. Bamerni, A. Kilicman
doaj   +1 more source

Analytic Automorphisms and Transitivity of Analytic Mappings

Mathematics, 2020
In this paper, we investigate analytic automorphisms of complex topological vector spaces and their applications to linear and nonlinear transitive operators.
Zoriana Novosad, Andriy Zagorodnyuk
doaj   +1 more source

Existence and nonexistence of hypercyclic semigroups [PDF]

, 2007
In these notes we provide a new proof of the existence of a hypercyclic uniformly continuous semigroup of operators on any separable infinitedimensional Banach space that is very different from –and considerably shorter than– the one recently given by ...
Bernal González, Luis, Grosse-Erdmann, Karl-Goswin   +1 more
core  

G- Cyclicity And Somewhere Dense Orbit

مجلة بغداد للعلوم, 2010
let H be an infinite – dimensional separable complex Hilbert space, and S be a multiplication semigroup of  with 1. An operator T is called G-cyclic over S if there is a non-zero vector xÎ H such that {aTn  x½aÎS, n ≥0} is norm-dense in H.
Zeana Zaki Jamil
doaj   +1 more source