Free Multivariate w*-Semicrossed Products: Reflexivity and the Bicommutant Property

Abstract

AbstractWe study w*-semicrossed products over actions of the free semigroup and the free abelian semigroup on (possibly non-selfadjoint) w*-closed algebras. We show that they are reflexive when the dynamics are implemented by uniformly bounded families of invertible row operators. Combining with results of Helmer, we derive that w*-semicrossed products of factors (on a separableHilbert space) are reflexive. Furthermore, we show that w*-semicrossed products of automorphic actions on maximal abelian self adjoint algebras are reflexive. In all cases we prove that the w*-semicrossed products have the bicommutant property if and only if the ambient algebra of the dynamics does also.