Structural results for free Araki–Woods factors and their continuous cores

@article{Houdayer2010StructuralRF,
  title={Structural results for free Araki–Woods factors and their continuous cores},
  author={Cyril Houdayer},
  journal={Journal of the Institute of Mathematics of Jussieu},
  year={2010},
  volume={9},
  pages={741 - 767}
}
  • Cyril Houdayer
  • Published 7 December 2008
  • Mathematics
  • Journal of the Institute of Mathematics of Jussieu
Abstract We show that for any type III1 free Araki–Woods factor $\mathcal{M}$ = (HR, Ut)″ associated with an orthogonal representation (Ut) of R on a separable real Hilbert space HR, the continuous core M = $\mathcal{M}$ ⋊σR is a semisolid II∞ factor, i.e. for any non-zero finite projection q ∈ M, the II1 factor qM q is semisolid. If the representation (Ut) is moreover assumed to be mixing, then we prove that the core M is solid. As an application, we construct an example of a non-amenable… 
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