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A Transformation with Simple Spectrum which is not Rank One

Published online by Cambridge University Press:  20 November 2018

Andrés Del Junco
Andrés Del Junco*
Affiliation:
University of British Columbia, Vancouver, British Columbia
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Abstract

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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 3 , 01 June 1977 , pp. 655 - 663
Copyright
Copyright © Canadian Mathematical Society 1977

References

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