• Corpus ID: 238634746

Spectral estimates of dynamically-defined and amenable operator families

  title={Spectral estimates of dynamically-defined and amenable operator families},
  author={Siegfried Beckus and Alberto Takase},
For dynamically-defined operator families, the Hausdorff distance of the spectra is estimated by the distance of the underlying dynamical systems while the group is amenable. We prove that if the group has strict polynomial growth and both the group action and the coefficients are Lipschitz continuous, then the spectral estimate has a square root behavior or, equivalently, the spectrum map is 1 2 -Hölder continuous. We prove the behavior can be improved resulting in the spectrum map being… 


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