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Averages of unitary representations and weak mixing of random walks

Michael Lin, Rainer Wittmann (1995)

Studia Mathematica

Let S be a locally compact (σ-compact) group or semigroup, and let T(t) be a continuous representation of S by contractions in a Banach space X. For a regular probability μ on S, we study the convergence of the powers of the μ-average Ux = ʃ T(t)xdμ(t). Our main results for random walks on a group G are: (i) The following are equivalent for an adapted regular probability on G: μ is strictly aperiodic; U n converges weakly for every continuous unitary representation of G; U is weakly mixing for any...

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