Results 101 to 110 of about 1,093 (132)

Rotations of Hypercyclic and Supercyclic Operators

Integral Equations and Operator Theory, 2004
A (bounded linear) operator \(T\) on a Banach space \(X\) is called hypercyclic if there is a vector \(x \in X\) such that its orbit \(\{T^n(x) \;| \;n=0,1,2,... \}\) is dense in \(X\); the vector \(x\) is called hypercyclic for \(T\). The operator \(T\) is called supercyclic if \(\{ \alpha T^n(x) \;| \alpha \in \mathbb C, n \in \mathbb N \}\) is dense
León-Saavedra, Fernando, Müller, Vladimír   +1 more
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Powers of Hypercyclic Functions for Some Classical Hypercyclic Operators

Integral Equations and Operator Theory, 2007
We show that no power of any entire function is hypercyclic for Birkhoff’s translation operator on $$\mathcal{H}(\mathbb{C})$$ . On the other hand, we see that the set of functions whose powers are all hypercyclic for MacLane’s differentiation operator is a Gδ ...
R. M. Aron, J. A. Conejero, A. Peris, J. B. Seoane–Sepúlveda   +3 more
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Syndetically Hypercyclic Operators

Integral Equations and Operator Theory, 2005
A sequence \((T_n)_{n\geq 0}\) of bounded operators on a separable \(\mathcal{F}\)-space \(X\) is hypercyclic if there exists a vector \(x\) in \(X\) such that the set \(\{T_n x \; ; \; n\geq 0\}\) is dense in \(X\). An operator \(T\) on \(X\) is hypercyclic if the sequence \((T^n)_{n\geq 0}\) of its powers is hypercyclic.
Peris, Alfredo, Saldivia, Luis
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Faber-hypercyclic operators

Israel Journal of Mathematics, 2008
Let \(X\) be a complex infinite-dimensional separable Banach space and \(T\) be a bounded linear operator on \(X\). Let \(\Omega\) be a bounded domain of the complex plane whose boundary is a closed Jordan curve and \((F_n^{\Omega})_{n\geq 0}\) be the sequence of Faber polynomials of \(\Omega\).
Badea, Catalin, Grivaux, Sophie
openaire   +2 more sources

Multi-hypercyclic operators are hypercyclic

Mathematische Zeitschrift, 2001
An operator \(T\) on a separable complex Hilbert space \(\mathcal H\) space is said to be hypercyclic if there is a vector \(x\) such that the orbit \(\{T^nx: n=0,1,\ldots\}\) is dense in \(\mathcal H\). An operator is said to be supercyclic if there is a vector \(x\) such that the scalar multiples of the elements in the orbit are dense in \(\mathcal H\
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Pathological hypercyclic operators

Archiv der Mathematik, 2006
We exhibit a hypercyclic operator whose square is not hypercyclic. Our operator is necessarily unbounded since a result of S. Ansari asserts that powers of a hypercyclic bounded operator are also hypercyclic. We also exhibit an unbounded Hilbert space operator whose non-zero vectors are hypercyclic.
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Hypercyclic Conjugate Operators

Integral Equations and Operator Theory, 2006
We prove that for any weighted backward shift B = Bw on an infinite dimensional separable Hilbert space H whose weight sequence w = (wn) satisfies \( \sup_{n} {\left| {w_{1} w_{2} \ldots w_{n} } \right|} = \infty \), the conjugate operator \( C_{B} :S \mapsto BSB^{*} \) is hypercyclic on the space S(H) of self-adjoint operators on H provided with the ...
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Frequently hypercyclic operators

2011
The contents of this chapter are motivated by recent work on the application of ergodic theory to linear dynamics. While the technical difficulties involved prevent us from studying these tools here, we will discuss a new concept that has come out of these investigations, the frequently hypercyclic operators.
Karl-G. Grosse-Erdmann, Alfred Peris Manguillot   +1 more
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Hypercyclic and Chaotic Convolution Operators

Journal of the London Mathematical Society, 2000
Every convolution operator on a space of ultradifferentiable functions of Beurling or Roumieu type and on the corresponding space of ultradistributions is hypercyclic and chaotic (i.e., it is transitive and has a dense set of periodic points) when it is not a multiple of the identity.
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Existence of hypercyclic operators

2011
In this chapter we obtain, among other things, the Ansari–Bernal theorem that every infinite-dimensional separable Banach space supports a hypercyclic operator. In contrast, some infinite-dimensional separable Banach spaces do not support any chaotic operator. We also discuss here the richness of the set of hypercyclic operators in two ways: it forms a
Karl-G. Grosse-Erdmann, Alfred Peris Manguillot   +1 more
openaire   +1 more source