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 ? is supercyclic if there x such that, COrb(T,x) = {?Tnx : C, n 0}, dense in In this paper, we extend notion from single to subset L(X). We prove that most related proprieties supercyclicity case remains true for ?. This leads us obtain some results C-regularized groups operators.