Free Multivariate w*-Semicrossed Products: Reflexivity and the Bicommutant Property
AbstractWe 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.
1980 ◽
Vol 77
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pp. 344-350
2011 ◽
Vol 54
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pp. 411-421
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1990 ◽
Vol 4
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pp. 447-460
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1993 ◽
Vol 03
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pp. 335-347
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1993 ◽
Vol 36
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pp. 49-54
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2010 ◽
Vol 88
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pp. 205-230
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