On linear dynamics of sets of operators

Authors: MOHAMED AMOUCH, OTMANE BENCHIHEB

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.

Keywords: Orbit, hypercyclic sets of operators, hypercyclic Operators, $C_0$-semigroup, $C$-regularized group

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