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Rank and spectral multiplicity. (English) Zbl 0809.28013
Summary: For a dynamical system \((X,T,\mu)\), we investigate the connections between a metric invariant, the rank \(r(T)\), and a spectral invariant, the maximal multiplicity \(m(T)\). We build examples of systems for which the pair \((m(T),r(T))\) takes values \((m,m)\) for any integer \(m\geq 1\) or \((p- 1,p)\) for any prime number \(p\geq 3\).

MSC:
28D05 Measure-preserving transformations
47A35 Ergodic theory of linear operators
28D10 One-parameter continuous families of measure-preserving transformations
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