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)
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.
reflexivity, semicrossed product
47A15 - Invariant subspaces [See also 47A46]
47L65 - Crossed product algebras (analytic crossed products)
47L75 - Other nonselfadjoint operator algebras
47L80 - Algebras of specific types of operators (Toeplitz, integral, pseudodifferential, etc.)