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The group of eigenvalues of a rank one transformation. (English) Zbl 0833.28008
In an earlier paper [Can. Math. Bull. 37, No. 1, 29-36 (1994; Zbl 0793.28013)], the authors gave a description of the maximal spectral type of a rank one transformation $$T$$, as a certain generalized Riesz product. Apparently it was suggested by J.-F. Mela that this description is related to the group $$e(T)$$ of $$L^\infty$$-eigenvalues of $$T$$. These are the $$L^2$$-eigenvalues when the underlying space is of finite measure, but the usual cutting and stacking construction for rank one maps allows the resulting measure space to be $$\sigma$$-finite.
Several characterizations of $$e(T)$$ are given for rank one $$T$$, one of which is intimately related to the corresponding expression for the maximal spectral type of $$T$$.

##### MSC:
 28D05 Measure-preserving transformations 47A35 Ergodic theory of linear operators
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