V. Ya. Golodets
Approximately Transitive Actions of Abelian Groups and Spectrum
Preprint series: ESI preprints

MSC:

22B99 None of the above but in this section

46J10 Banach algebras of continuous functions, function algebras, See also {46E25}

Abstract: It is proved that any measure-preserving approximately transitive
(AT) action of a locally compact separable Abelian group on a
Lebesgue space has simple spectrum. The proof is based on
investigation of properties of nontransient product cocycles and
actions associated with them. We used our result that two nontransient
cocycles with isomorphic associated (Mackey) actions are
weakly equivalent.

Keywords: locally compact abelian group, approximately transitive action, spectrum