Weak Semiprojectivity in Purely Infinite SimpleC*-Algebras

Abstract

AbstractLetAbe a separable amenable purely infinite simpleC*-algebra which satisfies the Universal Coefficient Theorem. We prove thatAis weakly semiprojective if and only ifKi(A) is a countable direct sum of finitely generated groups (i= 0, 1). Therefore, ifAis such aC*-algebra, for any ε > 0 and any finite subset ℱ ⊂Athere existδ> 0 and a finite subset⊂Asatisfying the following: for any contractive positive linear mapL:A→B(for anyC*-algebraB) with ∥L(ab) –L(a)L(b)∥ <δfora,b∈there exists a homomorphismh:A→Bsuch that ∥h(a) –L(a)∥ < ε fora∈ ℱ.