A generalization of the Brown-Pearcy Theorem

Abstract

Abstract. Let A be a unital separable simple exact C*-algebra. Suppose that either 1. A is purely infinite, or 2. A ⊗ K has strict comparison of positive elements and stable rank one, and A has unique tracial state.Then for all X ∈ M (A ⊗ K ) , X is a commutator if and only if X does not have the form α1 M (A ⊗K ) + x , for some α ∈ C − {0} and for some x belonging to a proper ideal ofMathematics subject classification (2010): 46L35.