Pointwise inner automorphisms of almost periodic factors

TL;DR

This paper proves that for a broad class of nonamenable almost periodic type III_1 factors, every pointwise inner automorphism can be decomposed into an inner automorphism and a modular automorphism, confirming Haagerup-Stormer's conjecture.

Contribution

It establishes the validity of Haagerup-Stormer's conjecture for a large class of nonamenable almost periodic type III_1 factors, including McDuff and free Araki-Woods factors.

Findings

Pointwise inner automorphisms decompose into inner and modular automorphisms.

The result applies to all McDuff factors absorbing R_infinity.

The result also applies to all free Araki-Woods factors.

Abstract

We prove that a large class of nonamenable almost periodic type ${\rm III_1}$ factors $M$, including all McDuff factors that tensorially absorb $R_\infty$ and all free Araki-Woods factors, satisfy Haagerup-Stormer's conjecture (1988): any pointwise inner automorphism of $M$ is the composition of an inner and a modular automorphism.