2023/10/31 by José R. Carrión, Carrión, José R., Jorge Castillejos +11
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Quantum Mechanics and Applications #Spectral Theory in Mathematical Physics #math.OA #msc:46L35
paper · pdf · doi:10.48550/arxiv.2310.20594
138 pages. Small edits to made, including to statement of Corollary 9.9. Accepted to Memoirs of the AMS
openalex publication_date 2023/10/31 · openalex created_date 2025/10/10 · arxiv created 2026/07/29 · arxiv updated 2026/07/30 · openalex updated_date 2026/08/01
We introduce a new class of operator algebras -- tracially complete C*-algebras -- as a vehicle for transferring ideas and results between C*-algebras and their tracial von Neumann algebra completions. We obtain structure and classification results for amenable tracially complete C*-algebras satisfying an appropriate version of Murray and von Neumann's property gamma for II1 factors. In a precise sense, these results fit between Connes' celebrated theorems for injective II1 factors and the unital classification theorem for separable simple nuclear C*-algebras. The theory also underpins arguments for the known parts of the Toms-Winter conjecture.