Results 71 to 80 of about 106 (90)
On the set of hypercyclic vectors for the differentiation operator [PDF]
Israel Journal of Mathematics, 2010 Let $D$ be the differentiation operator $Df=f'$ acting on the Fréchet space $\H$ of all entire functions in one variable with the standard (compact-open) topology. It is known since 1950's that the set $H(D)$ of hypercyclic vectors for the operator $D$ is non-empty. We treat two questions raised by Aron, Conejero, Peris and Seoane-Sepúlveda whether the
Stanislav Shkarin, Shkarin Stanislav
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Algebrability of the set of hypercyclic vectors for backward shift operators [PDF]
Advances in Mathematics, 2020 We study the existence of algebras of hypercyclic vectors for weighted backward shifts on Fréchet sequence spaces that are algebras when endowed with coordinatewise multiplication or with the Cauchy product. As a particular case we obtain that the sets of hypercyclic vectors for Rolewicz's and MacLane's operators are algebrable.
Javier Falco, Karl-G Grosse-Erdmann
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2011
This chapter studies the existence of common hypercyclic vectors for families of operators. While countable families of hypercyclic operators on the same space automatically possess common hypercyclic vectors, this is no longer the case for uncountable families.
Karl-G. Grosse-Erdmann +1 more
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This chapter studies the existence of common hypercyclic vectors for families of operators. While countable families of hypercyclic operators on the same space automatically possess common hypercyclic vectors, this is no longer the case for uncountable families.
Karl-G. Grosse-Erdmann +1 more
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Frequently hypercyclic operators and vectors
Ergodic Theory and Dynamical Systems, 2007We study frequently hypercyclic operators, a natural new concept in hypercyclicity that was recently introduced by F. Bayart and S. Grivaux. We derive a strengthened version of their Frequent Hypercyclicity Criterion, which allows us to obtain examples of frequently hypercyclic operators in a straightforward way. Moreover, Bayart and Grivaux have noted
Bonilla, A., Grosse-Erdmann, Karl
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Common hypercyclic vectors for unilateral weighted shifts on ℓ2
Journal of Operator Theory, 2021Each w∈ℓ∞ defines a bacwards weighted shift Bw:ℓ2→ℓ2. A vector x∈ℓ2 is \textit{hypercyclic} for Bw if the set of forward iterates of x is dense in ℓ2. For each such w, the set HC(w) consisting of all vectors hypercyclic for Bw is Gδ. The set of \textit{common hypercyclic vectors} for a set W⊆ℓ∞ is the set HC∗(W)=⋂w∈WHC(w).
Konstantinos Beros, Paul B. Larson
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Hypercyclic Operators on Vector-Valued Hardy Spaces
Iranian Journal of Science and Technology, Transactions A: Science, 2018Let T be a bounded linear operator on a Banach space X and $$\varphi$$ be an analytic self-map of the unit disk $${\mathbb {D}}.$$
Hamid Rezaei, Javad Amini Ab Alvan
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Real Analysis Exchange, 2023
In the paper under review, the author studies the spaceability of the set of frequently hypercyclic vectors for dissipative composition operators of bounded distortion on \(L^p\), \(1\leq p
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In the paper under review, the author studies the spaceability of the set of frequently hypercyclic vectors for dissipative composition operators of bounded distortion on \(L^p\), \(1\leq p
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Small sets and hypercyclic vectors
2008The authors study the smallness of the set of non-hyperbolic vectors for weighted backward shifts on \(c_0(\mathbb N)\) or \(\ell ^p(\mathbb N)\) \((1\leq ...
Bayart, Frédéric +2 more
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Rank One Perturbation of Unitary Operators with Full Measure of Hypercyclic Vectors
Bulletin of the Malaysian Mathematical Sciences Society, 2022Zhijing Chen, Chen Zhijing
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Hypercyclic behaviour of operators in a hypercyclic
Journal of Functional Analysis, 2007Alfred Peris
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