Ranks of operators in simple C*-algebras

2009/12/03 by Dadarlat, Marius, Toms, Andrew S. · 1 citation
#46L35 #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.0912.0675

Abstract

Let A be a unital simple separable C*-algebra with strict comparison of positive elements. We prove that the Cuntz semigroup of A is recovered functorially from the Murray-von Neumann semigroup and the tracial state space T(A) whenever the extreme boundary of T(A) is compact and of finite covering dimension. Combined with a result of Winter, we obtain Z ⊗ A isomorphic to A whenever A moreover has locally finite decomposition rank. As a corollary, we confirm Elliott's classification conjecture under reasonably general hypotheses which, notably, do not require any inductive limit structure. These results all stem from our investigation of a basic question: what are the possible ranks of operators in a unital simple C*-algebra?

Cited by

• Centrally pure C*-algebras

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