On linear dynamics of sets of operators

Abstract

Let X be a complex topological vector space with dim(X) > 1 and B(X) the set of all continuous linearoperators on X. The concept of hypercyclicity for a subset of B(X) was introduced in [1]. In this work, we introducethe notion of hypercyclic criterion for a subset of B(X) . We extend some results known for a single operator andC0 -semigroup to a subset of B(X) and we give applications for C-regularized groups of operators.