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We prove results on ergodicity, i.e. on the property that the space is a direct sum of the kernel of an operator and the closure of its range, for closed linear operators A such that ${\left|\right|\alpha (\alpha -A)}^{-1}\left|\right|$ is uniformly bounded for all α > 0. We consider operators on Banach spaces which have the property that the space is complemented in its second dual space by a projection P. Results on ergodicity are obtained under a norm condition ||I - 2P|| ||I - Q|| < 2 where Q is a projection depending on the operator A....