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Noncommutative recurrence over locally compact Hausdorff groups

Richard de Beer·Rocco Duvenhage·Anton Stroh
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Abstract

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.

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Richard de Beer, Rocco Duvenhage, Anton Stroh. 2005-09-16. Noncommutative recurrence over locally compact Hausdorff groups. https://doi.org/10.1016/j.jmaa.2005.08.063

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