2010/05/05 by Netzer, Tim, Thom, Andreas
#11E25 #46L10 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1005.0822
We prove that every positive trace on a countably generated *-algebra can be approximated by positive traces on algebras of generic matrices. This implies that every countably generated tracial *-algebra can be embedded into a metric ultraproduct of generic matrix algebras. As a particular consequence, every finite von Neumann algebra with separable pre-dual can be embedded into an ultraproduct of tracial *-algebras, which as *-algebras embed into a matrix-ring over a commutative algebra.