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arXiv · 1810.12438

On Linear Dynamics of Sets of Operators

Mohamed Amouch·Otmane Benchiheb
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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 \cite{AKH}. 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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Mohamed Amouch, Otmane Benchiheb. 2018-10-29. On Linear Dynamics of Sets of Operators. https://arxiv.org/abs/1810.12438

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