Results 61 to 70 of about 3,099 (194)
HYPERCYCLICITY OF OPERATORS THAT $$\lambda$$-COMMUTE WITH THE HARDY BACKWARD SHIFT
Journal of Mathematical SciencesAn operator T acting on a separable complex Banach space $$\mathcal {B}$$ B is said to be hypercyclic if there exists $$f\in \mathcal {B}$$ f ∈ B
M. Amouch +2 more
semanticscholar +1 more source
On operators T such that f(T) is hypercyclic [PDF]
Studia Mathematica, 1994 Summary: A bounded linear operator \(A\) on a complex, separable, infinite- dimensional Banach space \(X\) is called hypercyclic if there is a vector \(x\in X\) such that \(\{x, Ax, A^ 2 x,\dots\}\) is dense in \(X\). Let \(T\) be a bounded linear operator on \(X\) such that \(T\) is surjective and its generalized kernel \(\bigcup_{n\geq 1} N(T^ n ...
Herzog, Gerd, Schmoeger, Christoph
openaire +4 more sources
Dynamics of multivalued linear operators
Open Mathematics, 2017 We introduce several notions of linear dynamics for multivalued linear operators (MLO’s) between separable Fréchet spaces, such as hypercyclicity, topological transitivity, topologically mixing property, and Devaney chaos.
Chen Chung-Chuan +3 more
doaj +1 more source
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
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 +1 more
core
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
On Some Subspace Codiskcyclic Operators in Banach Spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.This paper introduces the concepts of subspace codiskcyclicity and subspace codisk transitivity, providing criteria and examples that highlight their distinct properties compared to traditional codiskcyclic operators and hypercyclic operators. The paper also demonstrates the existence of subspace codiskcyclic operators in finite‐dimensional Banach ...
Peter Masong Slaa +3 more
wiley +1 more source
The Strong Disjoint Blow‐Up/Collapse Property
Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013 Let X be a topological vector space, and let ℬ(X) be the algebra of continuous linear operators on X . The operators T1, …, TN ∈ ℬ(X) are disjoint hypercyclic if there is x ∈ X such that the orbit {(T1n(x),…,TNn(x)):n∈ℕ} is dense in X × …×X . Bès and Peris have shown that if T1, …, TN satisfy the Disjoint Blow‐up/Collapse property, then they are ...
Héctor N. Salas, Ajda Fošner
wiley +1 more source
Frequently hypercyclic operators with irregularly visiting orbits
, 2018 We prove that a bounded operator $T$ on a separable Banach space $X$ satisfying a strong form of the Frequent Hypercyclicity Criterion (which implies in particular that the operator is universal in the sense of Glasner and Weiss) admits frequently ...
Grivaux, Sophie
core +2 more sources
On the Existence of Polynomials with Chaotic Behaviour
Journal of Function Spaces, Volume 2013, Issue 1, 2013., 2013 We establish a general result on the existence of hypercyclic (resp., transitive, weakly mixing, mixing, frequently hypercyclic) polynomials on locally convex spaces. As a consequence we prove that every (real or complex) infinite‐dimensional separable Frèchet space admits mixing (hence hypercyclic) polynomials of arbitrary positive degree.
Nilson C. Bernardes Jr. +2 more
wiley +1 more source