Results 1 to 10 of about 123 (117)

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.
Z.H. Mozhyrovska
doaj   +3 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 ...
E Matheron
exaly   +3 more sources

ε-hypercyclic operators that are not δ-hypercyclic for δ < ε

Journal of Mathematical Analysis and Applications
For every fixed $ε$ $\in$ (0, 1), we construct an operator on the separable Hilbert space which is $δ$-hypercyclic for all $δ$ $\in$ ($ε$, 1) and which is not $δ$-hypercyclic for all $δ$ $\in$ (0, $ε$).
Frédéric Bayart
exaly   +2 more sources

Hypercyclicity of adjoint of convex weighted shift and multiplication operators on Hilbert spaces [PDF]

Mathematics and Computational Sciences, 2021
A bounded linear operator $T$ on a Hilbert space $\mathfrak{H}$ is convex, if $$\|\mathfrak{T}^{2}v\|^2-2\|\mathfrak{T}v\|^2+\|v\|^2 \geq 0.$$ In this paper, sufficient conditions to hypercyclicity of adjoint of unilateral (bilateral) forward (backward ...
Lotfollah Karimi
doaj   +1 more source

About Subspace-Frequently Hypercyclic Operators [PDF]

Sahand Communications in Mathematical Analysis, 2020
In this paper, we introduce subspace-frequently hypercyclic operators. We show that these operators are subspace-hypercyclic and there are subspace-hypercyclic  operators that are not subspace-frequently hypercyclic. There is a criterion like to subspace-
Mansooreh Moosapoor, Mohammad Shahriari
doaj   +1 more source

Notes on the Hypercyclic Operator

Journal of Mathematical Extension, 2008
In this paper by using a nice criterion, we show that the perturbation of identity operators by some multiples of the standard backward shift is hypercyclic. This gives a new proof for Salas Theorem in ( [10 ], Theorem 3.3).
H. Rezaei
doaj   +1 more source

Hypercyclic Toeplitz Operators [PDF]

Results in Mathematics, 2016
Minor corrections.
Anton Baranov, Andrei Lishanskii
openaire   +3 more sources

Frequently hypercyclic operators [PDF]

Transactions of the American Mathematical Society, 2006
We investigate the subject of linear dynamics by studying the notion of frequent hypercyclicity for bounded operators T T ...
Bayart, Frédéric, Grivaux, Sophie
openaire   +2 more sources

Multiples of hypercyclic operators [PDF]

Proceedings of the American Mathematical Society, 2008
We give a negative answer to a question of Prăjitură by showing that there exists an invertible bilateral weighted shift T T
Badea, Catalin, Grivaux, Sophie, Müller, Vladimir   +2 more
openaire   +4 more sources

On invertible hypercyclic operators [PDF]

Proceedings of the American Mathematical Society, 1992
Let A A be an invertible (bounded linear) operator acting on a complex Banach space
Herrero, Domingo A., Kitai, Carol
openaire   +2 more sources