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

TL;DR

This paper establishes a non-commutative version of the Weyl-von Neumann theorem for representations of AH algebras into semifinite von Neumann factors, extending classical results to a broader operator algebra context.

Contribution

It introduces a non-commutative approximation theorem for AH algebra representations into semifinite von Neumann factors, generalizing classical operator algebra results.

Findings

Proves a non-commutative Weyl-von Neumann theorem for semifinite von Neumann factors.

Establishes approximate summand results for finite von Neumann factors.

Extends classical representation equivalence results to a non-commutative setting.

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 ${\rm C}^{\ast}$-algebra. We also prove a result for approximate summands of representations of unital, separable AH algebras into finite von Neumann factors.