Approximation properties and absence of Cartan subalgebra for free Araki–Woods factors

We show that all the free Araki–Woods factors Γ ( H R , U t ) ″ have the complete metric approximation property. Using Ozawa–Popaʼs techniques, we then prove that every nonamenable subfactor N ⊂ Γ ( H R , U t ) ″ which is the range of a normal conditional expectation has no Cartan subalgebra. We fin...

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Veröffentlicht in:	Advances in mathematics (New York. 1965) 2011-10, Vol.228 (2), p.764-802
Hauptverfasser:	Houdayer, Cyril, Ricard, Éric
Format:	Artikel
Sprache:	eng
Schlagworte:	Cartan subalgebras Complete metric approximation property Deformation/rigidity Free probability Functional Analysis Mathematics Type III factors
Online-Zugang:	Volltext
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