Singular MASAs in type III factors and Connes' Bicentralizer Property

Cyril Houdayer; Sorin Popa

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Singular MASAs in type III factors and Connes' Bicentralizer Property

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arxiv 1704.07255 v3 pith:ZAW6W6W4 submitted 2017-04-24 math.OA

Cyril Houdayer , Sorin Popa This is my paper · ORCID

classification math.OA

keywords typebicentralizerconnesfactorspropertysingularabelianconditional

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abstract

We show that any type ${\rm III_1}$ factor with separable predual satisfying Connes' Bicentralizer Property (CBP) has a singular maximal abelian $\ast$-subalgebra that is the range of a normal conditional expectation. We also investigate stability properties of CBP under finite index extensions/restrictions of type ${\rm III_1}$ factors.

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