LAUSR

We prove a van der Corput-type lemma for power bounded Hilbert space operators. As a corollary we show that $$N^{-1}\sum _{n=1}^N T^{p(n)}$$N-1∑n=1NTp(n) converges in the strong operator topology for all power bounded Hilbert space operators T and all polynomials p satisfying $$p(\mathbb {N}_0)\subset \mathbb {N}_0$$p(N0)⊂N0. This generalizes known results for Hilbert space contractions. Similar results are true also for bounded strongly continuous semigroups of operators.