Singular MASAs in type III factors and Connes' Bicentralizer Property

Abstract

We show that any type $\mathrm{II}{\mathrm{I}}_1$ 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 $\mathrm{II}{\mathrm{I}}_1$ factors.

arXiv comment10 pages. To appear in the Proceedings of the 9th MSJ-SI "Operator Algebras and Mathematical Physics" held in Sendai, Japan (2016)