  It is folklore that a power bounded operator on a sequentially complete
locally convex space generates a uniformly continuous $C_0$-semigroup which is
given by the corresponding power series representation. Recently, Doma\'nski
asked if in this result the assumption of being power bounded can be relaxed.
We employ conditions introduced by \.{Z}elazko to give a weaker but still
sufficient condition for generation and apply our results to operators on
classical function and sequence spaces.
