UNIFORMLY ERGODIC THEOREM FOR SEMIGROUPS WITH k-DECOMPOSABLE KATO INFINITESIMAL GENERATORS
In this paper we shall extend the technical assumption (E − k) to semigroups. We prove that if T = (T(t),t ≥ 0) is C0-semigroup of operators in L(X) with k-decomposable Kato infinitesimal generator A satisfying the condition (E − k), then T is uniformly ergodic. These results are of interest in view of recent activity in the ergodic theory and its applications.
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