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

Robbie Bickerton, Evgenios Kakariadis

Research output: Contribution to journalArticlepeer-review


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 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.
Original languageEnglish
Pages (from-to)1201-1235
Number of pages34
JournalCanadian Journal of Mathematics
Issue number6
Early online date20 Nov 2018
Publication statusPublished - 1 Dec 2018


  • Reflexivity
  • Semicrossed products


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