We generalize two theorems about K-automorphisms from ℤ to all amenable groups with good entropy theory (this class includes all unimodular amenable groups which are not an increasing union of compact subgroups). The first theorem is that such actions are uniformly mixing; the second is that their spectrum is Lebesgue with countable multiplicity. For the proof we will develop an entropy theory for discrete amenable equivalence relations.
|Original language||English (US)|
|Number of pages||7|
|Journal||Electronic Research Announcements of the American Mathematical Society|
|State||Published - Jun 10 2005|
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