2015/03/26 by James Gabe, Gabe, James, Efren Ruiz +1 · 6 citations
Mathematics · #46L05 #46L35 #46L80 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algorithm #Cone (formal languages) #Convex cone #Convex optimization #FOS: Mathematics #Geometry #Mathematics #Operator (biology) #Operator Algebras (math.OA) #Operator algebra #Pure mathematics #Quotient #Regular polygon #Representation (politics) #Subderivative #Type (biology) #math.OA #msc:46L05 #msc:46L35 #msc:46L80
paper · pdf · doi:10.48550/arxiv.1503.07799
published in arXiv (Cornell University) (Cornell University) · 71 pages. V2: minor general changes, changed definition of X-C*-algebras
openalex publication_date 2015/03/26 · arxiv created 2015/10/15 · arxiv updated 2015/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We initiate the study of absorbing representations of C^∗-algebras with respect to closed operator convex cones. We completely determine when such absorbing representations exist, which leads to the question of characterising when a representation is absorbing, as in the classical Weyl-von Neumann type theorem of Voiculescu. In the classical case, this was proven by Elliott and Kucerovsky who proved that a representation is nuclearly absorbing if and only if it induces a purely large extension. By considering a related problem for extensions of C^∗-algebras, which we call the purely large problem, we ask when a purely largeness condition similar to the one defined by Elliott and Kucerovsky, implies absorption with respect to some given closed operator convex cone. We solve this question for a special type of closed operator convex cone induced by actions of finite topological spaces on C^∗-algebras. As an application of this result, we give K-theoretic classification for certain C^∗-algebras containing a purely infinite, two-sided, closed ideal for which the quotient is an AF algebra. This generalises a similar result by the second author, S. Eilers and G. Restorff in which all extensions had to be full.