Abstract
Following [10] an ergodic measure-preserving transformation is called rank one if it admits a sequence of approximating stacks. Rank one transformations have been studied in [1] and [2] where it was shown that any rank one transformation has simple spectrum. More generally it has been shown by Chacon [4] that a transformation of rank n has spectral multiplicity at most n. M. A. Akcoglu and J. R. Baxter have asked whether the converse is true. In particular: does simple spectrum imply rank one? In this paper we give a negative answer to this question.
Publisher
Canadian Mathematical Society
Cited by
28 articles.
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