Some versions of supercyclicity for a set of operators

Let X be a complex topological vector space and L(X) the set of all continuous linear operators on X. An operator T ? L(X) is supercyclic if there is x ? X such that, COrb(T,x) = {?Tnx : ? ? C, n ? 0}, is dense in X. In this paper, we extend this notion from a single operator T ? L(X) to a subset of operators ? ? L(X). We prove that most of related proprieties to supercyclicity in the case of a single operator T remains true for subset of operators ?. This leads us to obtain some results for C-regularized groups of operators.