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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 \(T\).

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