2007/04/30 by Nathanial P. Brown, Brown, Nathanial P., Andrew S. Toms +1 · 1 citation
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #math.OA
paper · pdf · doi:10.48550/arxiv.0704.3988
10 pages
arxiv created 2007/04/30 · openalex publication_date 2007/04/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Building on work of Elliott and coworkers, we present three applications of the Cuntz semigroup: (i) for many simple C^*-algebras, the Thomsen semigroup is recovered functorially from the Elliott invariant, and this yields a new proof of Elliott's classification theorem for simple, unital AI algebras; (ii) for the algebras in (i), classification of their Hilbert modules is similar to the von Neumann algebra context; (iii) for the algebras in (i), approximate unitary equivalence of self-adjoint operators is characterised in terms of the Elliott invariant.