On Stability of C*-Algebras

Abstract

LetAbe aσ-unital C*-algebra, i.e.,Aadmits a countable approximate unit. It is proved thatAis stable, i.e.,Ais isomorphic toA⊗K where K is the algebra of compact operators on a separable Hilbert space, if and only if for each positive elementa∈Aand eachε>0 there exists a positive elementb∈Asuch that ab