Linear Maps on C*-Algebras Preserving the Set of Operators that are Invertible in A/J

Abstract

For C*-algebras A of real rank zero, we describe linear maps phi on A that are surjective up to ideals J, and pi(A) is invertible in A/J if and only if pi(phi(A)) is invertible in A/J, where A is an element of A and pi: A -> A/J is the quotient map. We also consider similar linear maps preserving zero products on the Calkin algebra.