Growth order and stability of discrete semigroups Original Research Article

Characterizations of the growth order and the stability for the orbit {Tnx}{Tnx} of the powers TnTn of a bounded linear operator TT in terms of Cesàro and Abel means of the orbit are obtained. It is also seen that, under the Tauberian condition n‖Tn+1−Tn‖=O(1)n‖Tn+1−Tn‖=O(1), the strong (resp. uniform) convergence of {Tn}{Tn} is equivalent to its strong (resp. uniform) Abel mean convergence.