Pointwise inner automorphisms of almost periodic factors

Abstract

We prove that a large class of nonamenable almost periodic type $\mathrm{II}{\mathrm{I}}_1$ 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.

16 pages

References in corpus (2)

• Classification of a family of non almost periodic free Araki-Woods factors
• Fullness and Connes' $\mathbf{\tau }$ invariant of type III tensor product factors