Exponential Rank of C*-Algebras with Real Rank Zero and the Brown-Pedersen Conjectures

Abstract

We show that every C*-algebra with real rank zero has exponential rank ≤ 1 + ϵ. Consequently, C*-algebras with real rank zero have the property weak (FU). We also show that if A is a σ-unital C*-algebra with real rank zero, stable rank one, and trivial K 1-group then its multiplier algebra has real rank zero. If A is a σ-unital stable C*-algebra with stable rank one, we show that its multiplier algebra has real rank zero if and only if A has real rank zero and K 1 ( A) = 0.