Abstract :
We give a sufficient condition for the validity of the implication lim nª` T n xs0
« `ns0T n x converges, where T: XªX is a bounded linear operator, X is a
Banach space, and xgX. From this condition we derive the results given by other
authors. Moreover, we give some properties about the operators that verifies the
above implication, which are called Neumann operators.
