Results 131 to 140 of about 491,446 (159)

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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A short proof of existence of disjoint hypercyclic operators [PDF]

Journal of Mathematical Analysis and Applications, 2010
We give a short proof of existence of disjoint hypercyclic tuples of operators of any given length on any separable infinite dimensional Fr\'echet space.
Stanislav Shkarin
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Convolution operators supporting hypercyclic algebras [PDF]

Journal of Mathematical Analysis and Applications, 2017
[EN] We show that any convolution operator induced by a non-constant polynomial that vanishes at zero supports a hypercyclic algebra. This partially solves a question raised by R.
Juan Bes, J Alberto Conejero
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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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On the spectrum of supercyclic/hypercyclic operators [PDF]

Advances in Operator Theory
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 ...
Pietro Aiena, Salvatore Triolo
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Residuality of Sets of Hypercyclic Operators

Integral Equations and Operator Theory, 2011
Let \(X\) be a separable metrizable topological vector space and let \(L(X)\) denote the set of continuous and linear operators from \(X\) to \(X\). An operator \(T\in L(X)\) is called \textit{hypercyclic} if there exists a vector \(x\in X\) such that \(\{T^n x:n\in\mathbb{N}\}\) is dense in \(X\), and it is said to be \textit{supercyclic} if there ...
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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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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
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A strictly weakly hypercyclic operator with a hypercyclic subspace

Journal of Operator Theory
An interesting topic of study for a hypercyclic operator T:X→X on a topological vector space X has been whether X has an infinite\hyp{}dimensional, closed subspace consisting entirely, except for the zero vector, of hypercyclic vectors of T. These subspaces are called hypercyclic subspaces. It has been known that there is an operator T:H→H on a Hilbert
Chan, Kit C., Madarasz, Zeno
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Hypercyclic and chaotic operators

2011
In this chapter, the notions and results from the first chapter are revisited in the context of linearity. We introduce the notion of a hypercyclic operator and that of a chaotic operator. Among other things it is proved that the classical operators of Birkhoff, MacLane and Rolewicz are chaotic; it is shown that every hypercyclic operator possesses a ...
Karl-G. Grosse-Erdmann, Alfred Peris Manguillot   +1 more
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