摘要
Characterizations of the growth order and the stability for the orbit {T n x} of the powers T n of a bounded linear operator T in terms of Cesàro and Abel means of the orbit are obtained. It is also seen that, under the Tauberian condition n {norm of matrix} T n + 1 - T n {norm of matrix} = O (1), the strong (resp. uniform) convergence of {T n } is equivalent to its strong (resp. uniform) Abel mean convergence. © 2009 Elsevier Ltd. All rights reserved.