2012/02/14 by Andre Kornell, Kornell, Andre
Physics and Astronomy · #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Mechanics and Applications
paper · pdf · doi:10.48550/arxiv.1202.2994
openalex publication_date 2012/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop the viewpoint that the opposite of the category of W*-algebras and unital normal *-homomorphisms is analogous to the category of sets and functions. For each pair of W*-algebras, we construct their free exponential, which in the context of this analogy corresponds to the collection of functions from one of these W*-algebras to the other. We also show that every unital normal completely positive map between W*-algebras arises naturally from a normal state on their free exponential.