Abstract
We show that any type $\mathrm{III}_1$ 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 $\mathrm{III}_1$ factors.
Information
Published: 1 January 2019
First available in Project Euclid: 21 August 2019
zbMATH: 07116424
MathSciNet: MR3966585
Digital Object Identifier: 10.2969/aspm/08010109
Subjects:
Primary:
46L10
,
46L36
Keywords:
Connes' bicentralizer property
,
Singular maximal abelian $\ast$-subalgebras
,
Type $\mathrm{III}$ factors
Rights: Copyright © 2019 Mathematical Society of Japan
