# Singular MASAs in type III factors and Connes' Bicentralizer Property

## TL;DR

This paper demonstrates that type III_1 factors with separable predual satisfying Connes' Bicentralizer Property contain a singular MASA as the range of a normal conditional expectation, and explores CBP stability under finite index extensions.

## Contribution

It establishes the existence of singular MASAs in type III_1 factors with CBP and analyzes their stability under finite index extensions and restrictions.

## Key findings

- Existence of singular MASAs in type III_1 factors with CBP
- Stability of CBP under finite index extensions/restrictions
- Characterization of MASAs as ranges of normal conditional expectations

## 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.