Results 81 to 90 of about 752 (101)

Common Hypercyclic Vectors and the Hypercyclicity Criterion

Integral Equations and Operator Theory, 2009
An operator on a separable, infinite dimensional Banach space satisfies the Hypercyclicity Criterion if and only if the associated left multiplication operator is hypercyclic; see [14], [16], [29]. By examining paths of operators where each operator along the path satisfies the criterion, we provide necessary and sufficient conditions for a path of ...
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Frequently hypercyclic operators and vectors

Ergodic Theory and Dynamical Systems, 2007
We 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
A. BONILLA, K.-G. GROSSE-ERDMANN
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Common hypercyclic vectors

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, Alfred Peris Manguillot   +1 more
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Common hypercyclic vectors for unilateral weighted shifts on ℓ2

Journal of Operator Theory, 2021
Each 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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Rank One Perturbation of Unitary Operators with Full Measure of Hypercyclic Vectors

Bulletin of the Malaysian Mathematical Sciences Society, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, Xin, Chen, Zhijing
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Hypercyclic Operators on Vector-Valued Hardy Spaces

Iranian Journal of Science and Technology, Transactions A: Science, 2018
Let 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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On the Existence of Infinite-Dimensional Closed Subspaces of Frequently Hypercyclic Vectors for $T_f$

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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Small sets and hypercyclic vectors

2008
The 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, Matheron, Etienne, Moreau, Pierre   +2 more
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