Some Properties of Γ-supercyclic operators

الملخص

In this paper, we define Γ-transitive operators to study some further properties of Γ-supercyclic operators. In particular, we study Γ-supercyclic criterion which is a set of some sufficient conditions for an operator to be Γ-supercyclic. We use these conditions to partially answer an open problem in the literature. In particular, we show that if Γ =  ???????? and  ???? satisfies Γ-criterion, then ???? is supercyclic.