• Corpus ID: 116988927

EXISTENCE OF COMMON HYPERCYCLIC VECTORS FOR TRANSLATION OPERATORS

@article{Tsirivas2014EXISTENCEOC,
  title={EXISTENCE OF COMMON HYPERCYCLIC VECTORS FOR TRANSLATION OPERATORS},
  author={N. Tsirivas},
  journal={arXiv: Complex Variables},
  year={2014}
}
  • N. Tsirivas
  • Published 28 November 2014
  • Mathematics
  • arXiv: Complex Variables
Let H(C) be the set of entire functions endowed with the topology Tu of local uniform convergence. Fix a sequence of non-zero complex numbers (�n) with |�n| → +∞ and |�n+1|/|�n| → 1. We prove that there exists a residual set G ⊂ H(C) such that for every f ∈ G and every non-zero complex number a the set {f(z + �na) : n = 1,2,...} is dense in (H(C),Tu). This provides a very strong extension of a theorem due to Costakis and Sambarino in (23). Actually, in (23) the above result is proved only for… 
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References

SHOWING 1-10 OF 38 REFERENCES
Remarks on common hypercyclic vectors
Abstract We treat the question of existence of common hypercyclic vectors for families of continuous linear operators. It is shown that for any continuous linear operator T on a complex Frechet space
Genericity of wild holomorphic functions and common hypercyclic vectors
Abstract Let Tα be the translation operator by α in the space of entire functions H ( C ) defined by T α ( f )(z)=f(z+α) . We prove that there is a residual set G of entire functions such that for
Hypercyclic and Cyclic Vectors
Abstract 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. (1) An
Common Hypercyclic Vectors for the Conjugate Class of a Hypercyclic Operator
Abstract Given a separable, infinite dimensional Hilbert space, it was recently shown by the authors that there is a path of chaotic operators, which is dense in the operator algebra with the strong
Universal elements for non-linear operators and their applications
Abstract We prove that under certain topological conditions on the set of universal elements of a continuous map T acting on a topological space X, that the direct sum T ⊕ M g is universal, where M g
Rotations of Hypercyclic and Supercyclic Operators
Abstract.Let T  ∈  B(X) be a hypercyclic operator and λ a complex number of modulus 1. Then λ T is hypercyclic and has the same set of hypercyclic vectors as T. A version of this results gives for a
Frequently hypercyclic operators
We investigate the subject of linear dynamics by studying the notion of frequent hypercyclicity for bounded operators T on separable complex F-spaces: T is frequently hypercyclic if there exists a
TWO CRITERIA FOR A PATH OF OPERATORS TO HAVE COMMON HYPERCYCLIC VECTORS
We offer two conditions for a path of bounded linear operators on a Banach space to have a dense Gd set of common hypercyclic vectors. One of them is an equivalent condition and the other one is a
Universal vectors for operators on spaces of holomorphic functions
A vector x in a linear topological space X is called universal for a linear operator T on X if the orbit {Tnx: n > 0} is dense in X. Our main result gives conditions on T and X which guarantee that T
ON UNIVERSAL FUNCTIONS
An entire function is called universal with respect to translations if for any $g\;{\in}\;H(\mathbb{C}),\;R\;>\;0,\;and\;{\epsilon}\;>\;0$, there is such that $f(z\;+\;n)\;-\;g(z)\;z\;{\leq}\;R$.
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