Convergence of certain subsequences of the power sequence in a Banach algebra

Dragan S Djordjević, Milica Z Kolundžija, Mehdi Mohammadzadeh Karizaki

We consider the existence of limits lim n→∞ a qn and lim n→∞ a q n , where a is an arbitrary element of a complex Banach algebra with the unit, and q is an integer, q ≥ 2.