Approximate equivalence of representations of AH algebras into semifinite von Neumann factors

Abstract

In this paper, we prove a non-commutative version of the Weyl–von Neumann theorem for representations of unital, separable AH algebras into countably decomposable, semifinite, properly infinite, von Neumann factors, where an AH algebra means an approximately homogeneous $C^{\ast }$-algebra. We also prove a result for approximate summands of representations of unital, separable AH algebras into finite von Neumann factors.