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arXiv · 1701.02564

Free multivariate w*-semicrossed products: reflexivity and the bicommutant property

Robert T. Bickerton·Evgenios T. A. Kakariadis
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Abstract

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 over 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 so does the ambient algebra of the dynamics.

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Robert T. Bickerton, Evgenios T. A. Kakariadis. 2017-07-09. Free multivariate w*-semicrossed products: reflexivity and the bicommutant property. https://arxiv.org/abs/1701.02564

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