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

Don Hadwin; Rui Shi

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arXiv · 1801.02510

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

Don Hadwin·Rui Shi

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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.

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Don Hadwin, Rui Shi. 2018-01-08. A note on the Voiculescu's theorem for commutative C$^*$-algebras in semifinite von Neumann algebras. https://arxiv.org/abs/1801.02510

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