Approximate equivalence in von Neumann algebras  

作　　者：DING Huiru Don Hadwin 

机构地区：[1]Department of Mathematics,University of New Hampshire,Durham,NH03824,USA Department of Mathematics,University of New Hampshire,Durham,NH03824,USA

出　　处：《Science China Mathematics》2005年第2期239-247,共9页中国科学：数学（英文版）

摘　　要：One formulation of D. Voiculescu's theorem on approximate unitary equivalence is that two unital representations π and ρ of a separable C*-algebra are approximately unitarily equivalent if and only if rank οπ = rank ορ. We study the analog when the ranges of π and ρ are contained in a von Neumann algebra R, the unitaries inducing the approximate equivalence must come from R, and 'rank' is replaced with 'R -rank' (defined as the Murray-von Neumann equivalence of the range projection).One formulation of D. Voiculescu's theorem on approximate unitary equivalence is that two unital representations π and ρ of a separable C*-algebra are approximately unitarily equivalent if and only if rank o π = rank o ρ. We study the analog when the ranges of π and ρ are contained in a von Neumann algebra R, the unitaries inducing the approximate equivalence must come from R, and "rank" is replaced with "R-rank" (defined as the Murray-von Neumann equivalence of the range projection).

关 键 词：APPROXIMATE equivalence  R-rank. 

分 类 号：N[自然科学总论]