Look: it’s GNS Hilbert spaces everywhere!

I was asked to give a talk at the conference Geometry and Dynamics in honour of Beppe Marmo’s 80th birthday in Naples (go to the slides).

Based on:

F.M. Ciaglia, F. Di Cosmo, and L.E. González-Bravo: Can Čencov Meet Petz: Geometric Science of Information: 2023-08: doi: 10.1007/978-3-031-38299-4_38. Available at: https://arxiv.org/abs/2305.12482

F.M. Ciaglia, F. Di Nocera, J. Jost, and L. Schwachhöfer: Parametric models and information geometry on W*-algebras: Information geometry 7(1): 2024-01: doi: 10.1007/s41884-022-00094-6. Available at: https://arxiv.org/abs/2207.09396

F.M. Ciaglia, F. Di Cosmo, and L.E. González-Bravo: Fields of covariances on non-commutative probability spaces in finite dimensions: 2025-10: doi: 10.48550/arXiv.2510.24617. Available at: https://arxiv.org/abs/2510.24617

F.M. Ciaglia, F. Di Cosmo, and L.E. González-Bravo: Towards a category-theoretic foundation of classical and quantum information geometry: Geometric Science of Information: 2026: doi: 10.1007/978-3-032-03921-7_26. Available at: https://arxiv.org/abs/2509.10262