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Strong solidity of free Araki-Woods factors. (English) Zbl 1458.46050
Summary: We show that D. Shlyakhtenko’s free Araki-Woods factors [Pac. J. Math. 177, No. 2, 329–368 (1997; Zbl 0882.46026)] are strongly solid, meaning that for any diffuse amenable von Neumann subalgebra that is the range of a normal conditional expectation, the normalizer remains amenable. This provides the first class of nonamenable strongly solid type III factors.

MSC:
46L36 Classification of factors
46L10 General theory of von Neumann algebras
Citations:
Zbl 0882.46026
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