On the Equivalence Between Ergodicity and Weak Mixing for Operators Semigroups

Abstract

We prove the equivalence between ergodicity and weak mixing of an invariant probability measure m for strongly continuous contraction semigroups of linear operators on L 2 (m) satisfying the sector condition.The same result is proved for subordinated semigroups in the Bochner sense by the one-sided stable sudordinators.