Abstract
For a dynamical system (X, B, T, μ) we investigate the connections between metric invariants, the rankr(T) and the covering numberF *(T) and a spectral property for having a simple spectrum. Given a positive integerr≥2, a real numberb, 0<b<1 such thatr·b≥1, we construct examples of systems withr(T)=r, F *(T)=b and having a simple spectrum.
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Filipowicz, I., Kwiatkowski, J. Rank, covering number and a simple spectrum. J. Anal. Math. 66, 185–215 (1995). https://doi.org/10.1007/BF02788822
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DOI: https://doi.org/10.1007/BF02788822