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