SPECIAL AUTOMORPHISMS WITH CONTINUOUS SPECTRUM

Abstract

In this paper conditions are given for the primitive automorphism of a cyclic KS approximation to have continuous spectrum. If T: X → X admits a cyclic KS approximation with speed o(1/n) it is then shown that for a dense set of measurable sets A € ????, T^A: X^A → X^A is weakly mixing, i.e. has continuous spectrum. In particular it is shown that if T_α is an irrational rotation on the unit circle there exists an uncountable dense set of measurable sets for which (T^α)^A has continuous spectrum.