Ergodic results in operator algebras
Abstract
We provide a hierarchy of “nonconventional ergodic theorems” in quantum setting involving operators and unitaries acting on the Hilbert space of the Gelfand-Naimark-Segal covariant representation associated to a reference C*-dynamical system. The first two levels correspond to the Mean Ergodic Theorem by J. von Neumann involving a unitary, and the ergodic theorem by Kovács and Szúcs relative to unitarily implemented automorphisms of von Neumann algebras, respectively. As a consequence, we provide multiple correlation results concerning the ergodic behaviour of “three-operator” expectations.
Fields of Study & Subjects
Advanced Operator Algebra Research
Mathematical Dynamics and Fractals
Holomorphic and Operator Theory
Publication details
- Journal / source
- Utilitas Mathematica
- Volume
- 126
- Pages
- 105–123
- Publication date
- 27 January 2026
- Language
- EN