Prime type III factors.
It is shown that for each 0 < lambda < 1, the free Araki-Woods factor of type III(lambda) cannot be written as a tensor product of two diffuse von Neumann algebras (i.e., is prime) and does not contain a Cartan subalgebra.
Shlyakhtenko
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Department of Mathematics, University of California, Los Angeles, CA 90095, USA. shlyakht@math.ucla.edu