Lifting Algebraic Elements in C*-Algebras

Suppose J is a closed ideal in a unital C*-algebra A. This paper reduces the problem of lifting algebraic elements from A/J to A to the problem of lifting finite orthogonal families of projections. Such liftings are always possible when A has real rank zero. An application shown is that for every ϵ > 0 and for every nonzero polynomial p, there is a δ > 0 such that whenever a is a C*-element with ||a|| ≤1 and ||p(a)|| < δ, there is a b in C*(a) such that p(b) = 0 and ||b - a|| < ϵ.