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Free Araki-Woods factors and Connes’ bicentralizer problem

By Cyril Houdayer

Abstract

Abstract. We show that for any type III1 free Araki-Woods factor M = Γ(HR, Ut) ′ ′ , the bicentralizer of the free quasi-free state ϕU is trivial. Using Haagerup’s Theorem, it follows that there always exists a faithful normal state ψ on M such that (M ψ) ′ ∩ M = C. 1

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.310.9876
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