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

Bickerton, Robert T. ; Kakariadis, Evgenios T. A.

Canadian journal of mathematics, Tome 70 (2018) no. 6, pp. 1201-1235

Résumé

We study ${{\text{w}}^{*}}$ -semicrossed products over actions of the free semigroup and the free abelian semigroup on (possibly non-selfadjoint) ${{\text{w}}^{*}}$ -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 ${{\text{w}}^{*}}$ -semicrossed products of factors (on a separableHilbert space) are reflexive. Furthermore, we show that ${{\text{w}}^{*}}$ -semicrossed products of automorphic actions on maximal abelian self adjoint algebras are reflexive. In all cases we prove that the ${{\text{w}}^{*}}$ -semicrossed products have the bicommutant property if and only if the ambient algebra of the dynamics does also.

Détail

DOI : 10.4153/CJM-2017-031-0

Mots-clés : 47A15, 47L65, 47L75, 47L80, reflexivity, semicrossed product

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