Results 61 to 70 of about 1,090 (133)

On the Weakly Hypercyclic Composition Operators on Hardy Spaces

Journal of Mathematical Extension, 2010
An operator T on a Banach space X is said to be weakly hypercyclic if there exists a vector x ∈ X whose orbit under T is weakly dense in X. We show that every weakly hypercyclic composition operator on classic Hardy space H2 is norm hypercyclic.
H. Rezaei
doaj  

Operators with hypercyclic Cesaro means [PDF]

Studia Mathematica, 2002
Let \(T\) be a bounded linear operator on complex Banach space \(B\) and consider the arithmetic means \(M_n(T)= (I+ T+\cdots+ T^{n-1})/n\). The operator \(T\) is said to be hypercyclic if there exists a vector \(x\) in \(B\) such that the orbit \(\{T^n x\}\) is dense in \(B\).
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Topologically mixing hypercyclic operators [PDF]

Proceedings of the American Mathematical Society, 2003
Let X X be a separable Fréchet space. We prove that a linear operator T : X → X T:X\to X satisfying a special case of the Hypercyclicity Criterion is topologically mixing, i.e.
Costakis, George, Sambarino, Martín
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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

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 ...
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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
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Hypercyclic differentiation operators

, 1999
8 ...
Aron, Richard M., Bes, Juan P.
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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 \
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Invertible Subspace-Hypercyclic Operators

Journal of Mathematical Extension, 2015
A bounded linear operator on a Banach space X is called subspace-hypercyclic for a subspace M if Orb(T, x) \ M is dense in M for a vector x 2 M. In this paper we give conditions under which an operator is M-hypercyclic.
S. Talebi, B. Yousefi, M. Asadipour
doaj  

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