Approximate Equivalence in von Neumann Algebras

2020/08/15 by Li, Qihui, Hadwin, Don, Liu, Wenjing
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2008.06619

Abstract

Suppose A is a separable unital ASH C*-algebra, R is a sigma-finite II_∞ factor von Neumann algebra, and π,ρ:A\rightarrowR are unital ∗-homomorphisms such that, for every a\inA, the range projections of π( a) and ρ( a) are Murray von Neuman equivalent in R% . We prove that π and ρ are approximately unitarily equivalent modulo K_R, where K_R is the norm closed ideal generated by the finite projections in R. We also prove a very general result concerning approximate equivalence in arbitrary finite von Neumann algebras.

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