Noncommutative recurrence over locally compact Hausdorff groups

We extend previous results on noncommutative recurrence in unital ∗-algebras over the integers to the case where one works over locally compact Hausdorff groups. We derive a generalization of Khintchine’s recurrence theorem, as well as a form of multiple recurrence. This is done using the mean ergodic theorem in Hilbert space, via the GNS construction. © 2005 Elsevier Inc. All rights reserved