Uniqueness of extremal almost periodic states on the injective type III1 factor
Abstract
Abstract Let denote the Araki–Woods factor—the unique separable injective type factor. For extremal almost periodic states , we show that if and have the same point spectrum, then for some . Consequently, the extremal almost periodic states on are parameterized by countable dense subgroups of , up to precomposition by automorphisms. As an application, we show that KMS states for generalized gauge actions on Cuntz algebras agree (up to an automorphism) with tensor products of Powers states on their von Neumann completions.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Quantum chaos and dynamical systems
Mathematical functions and polynomials
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 5
- Publication date
- 1 May 2026
- Language
- EN