Results 71 to 80 of about 453,986 (139)

Hypercyclic Operators on Non-normable Fréchet Spaces [PDF]

, 1998
Every infinite dimensional separable non-normable Fréchet space admits a continuous hypercyclic operator. A large class of separable countable inductive limits of Banach spaces with the same property is given, but an example of a separable complete ...
Bonet, José, Peris, Alfredo
core   +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

On locally finite groups whose derived subgroup is locally nilpotent

Mathematische Nachrichten, Volume 297, Issue 12, Page 4389-4400, December 2024.
Abstract A celebrated theorem of Helmut Wielandt shows that the nilpotent residual of the subgroup generated by two subnormal subgroups of a finite group is the subgroup generated by the nilpotent residuals of the subgroups. This result has been extended to saturated formations in Ballester‐Bolinches, Ezquerro, and Pedreza‐Aguilera [Math. Nachr.
Marco Trombetti
wiley   +1 more source

Note on epsilon-cyclic operator

Ibn Al-Haitham Journal for Pure and Applied Sciences
In this paper, we investigated the concept of ε-diskcyclic operators on a separable infinite-dimensional Hilbert space . A bounded linear operator  is called -diskcyclic if there exists a vector in  such that its disk orbit  visits every cone of ...
Muammer Badree Abed, Zeana Zaki Jamil
doaj   +1 more source

On the spectrum of supercyclic/hypercyclic operators [PDF]

This paper concerns the spectral structure of hypercyclic and supercyclic operators defined on Banach spaces, or defined on Hilbert spaces. We also consider the spectral properties of operators in Hilbert spaces that commute with a hypercyclic operator ...
Aiena P., Triolo S., Burderi F.
core   +1 more source

Hypercyclic subspaces for Frechet space operators [PDF]

, 2006
A continuous linear operator T:X→X is hypercyclic if there is an x∈X such that the orbit {Tnx} is dense, and such a vector x is said to be hypercyclic for T.
Petersson, Henrik, Petersson, Henrik,
core   +1 more source

Dynamics, Operator Theory, and Infinite Holomorphy

, 2014
Abstract and Applied Analysis, Volume 2014, Issue 1, 2014.
Alfred Peris, Manuel Maestre, Miguel Martín, Yun Sung Choi   +3 more
wiley   +1 more source

Hypercyclic and Cyclic Vectors [PDF]

, 1995
Let X denote an arbitrary separable Banach space over the field of complex numbers and B(X) the Banach algebra of all bounded linear operators on X. We prove the following results.
Ansari, S.I.
core   +1 more source

СHAOTIC COMMUTATING WITH THE DUNKL DIFFERENTIATION LINEAR OPERATORS ON THE SPACE OF ANALYTIC FUNCTIONS

Вестник Донского государственного технического университета, 2018
We give representation of linea continuous operator, commutating with Dankle differentiation. These operators turn out to be chaotic and hypercyclic.
A.V. BRATISHCHEV
doaj