Maps with separable dynamics and the spectral properties of the operators generated by them
Journal: Sbornik Mathematics
Year: 2015

A map of a space X into itself generates weighted shift operators B in function spaces on X.The spectral properties of such operators are intimately connected with the dynamics of .It was known previously that the spectrum of an operator depends only on the set of invariant ergodic measures for .Conditions for the right invertibility of the operators B -I are obtained when is a spectral value.The main result states that right invertibility is only possible when a nontrivial attractor exists.