A note on the Voiculescu's theorem for commutative C$^*$-algebras in semifinite von Neumann algebras

Abstract: In the current paper, we generalize the "compact operator" part of the Voiculescu's non-commutative Weyl-von Neumann theorem on approximate equivalence of unital $$-homomorphisms of an commutative C$^$ algebra $\mathcal{A}$ into a semifinite von Neumann algebra. A result of D. Hadwin for approximate summands of representations into a finite von Neumann factor $\mathcal{R}$ is also extended.