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Bickerton, Robert T.; Kakariadis, Evgenios T.A.
Free Multivariate w*-Semicrossed Products: Reflexivity and the Bicommutant Property
We 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 separable Hilbert space) are reflexive. Furthermore we show that w*-semicrossed products of automorphic actions on maximal abelian selfadjoint 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.

Keywords:reflexivity, semicrossed product
Categories:47A15, 47L65, 47L75, 47L80

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