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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We also characterize simultaneous hypercyclic unilateral Rolewicz-type operators on $c_0(\N)$ and $\ell^p(\N)$, $p \in [1, \infty)$.
📌 3 Key Takeaways
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Objective & Hypothesis:We characterize disjoint hypercyclic and supercyclic tuples of unilateral Rolewicz-type operators on $c_0(\N)$ and $\ell^p(\N)$, $p \in [1, \infty)$, which are a generalization of the unilateral backward shift operator.
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Key Findings & Data:We show that disjoint hypercyclicity and disjoint supercyclicity are equivalent among a subfamily of these operators and disjoint hypercyclic unilateral Rolewicz-type operators always satisfy the Disjoint Hypercyclicity Criterion.
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Conclusion & Impact:We also characterize simultaneous hypercyclic unilateral Rolewicz-type operators on $c_0(\N)$ and $\ell^p(\N)$, $p \in [1, \infty)$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:hypercyclic vectors · hypercyclic operators · disjoint hypercyclicity
Abstract
We characterize disjoint hypercyclic and supercyclic tuples of unilateral Rolewicz-type operators on $c_0(\N)$ and $\ell^p(\N)$, $p \in [1, \infty)$, which are a generalization of the unilateral backward shift operator. We show that disjoint hypercyclicity and disjoint supercyclicity are equivalent among a subfamily of these operators and disjoint hypercyclic unilateral Rolewicz-type operators always satisfy the Disjoint Hypercyclicity Criterion. We also characterize simultaneous hypercyclic unilateral Rolewicz-type operators on $c_0(\N)$ and $\ell^p(\N)$, $p \in [1, \infty)$.
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Cite This Article
Çolakoğlu, N., Martin, Ö. (2021). Disjoint and simultaneous hypercyclic Rolewicz-type operators. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 6. https://doi.org/10.15672/hujms.791344