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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We extend some results known for a single operator and $C_0$-semigroup to a subset of $\mathcal{B}(X)$ and we give applications for $C$-regularized groups of operators.
📌 3 Key Takeaways
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Objective & Hypothesis:Let $X$ be a complex topological vector space with $dim(X)>1$ and $\mathcal{B}(X)$ the set of all continuous linear operators on $X$.
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Key Findings & Data:The concept of hypercyclicity for a subset of $\mathcal{B}(X)$ was introduced in [1].
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Conclusion & Impact:We extend some results known for a single operator and $C_0$-semigroup to a subset of $\mathcal{B}(X)$ and we give applications for $C$-regularized groups of operators.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Orbit · hypercyclic sets of operators · hypercyclic Operators
Abstract
Let $X$ be a complex topological vector space with $dim(X)>1$ and $\mathcal{B}(X)$ the set of all continuous linear operators on $X$. The concept of hypercyclicity for a subset of $\mathcal{B}(X)$ was introduced in [1]. In this work, we introduce the notion of hypercyclic criterion for a subset of $\mathcal{B}(X)$. We extend some results known for a single operator and $C_0$-semigroup to a subset of $\mathcal{B}(X)$ and we give applications for $C$-regularized groups of operators.
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Cite This Article
AMOUCH, M., BENCHIHEB, O. (2019). On linear dynamics of sets of operators. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 402–411. https://ajindex.com/articles/218058