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

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 ope...

Full description

Saved in:
Bibliographic Details
Published in:Canadian journal of mathematics 2018-12, Vol.70 (6), p.1201-1235
Main Authors: Bickerton, Robert T., Kakariadis, Evgenios T. A.
Format: Article
Language:English
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0008-414X
1496-4279
DOI:10.4153/CJM-2017-031-0