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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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