Stability of Real C * -Algebras

We will give a characterization of stable real C*-algebras analogous to the one given for complex C*-algebras by Hjelmborg and Rordam. Using this result, we will prove that any real C*-algebra satisfying the corona factorization property is stable if and only if its complexification is stable. Real C*-algebras satisfying the corona factorization property include AF-algebras and purely infinite C*-algebras. We will also provide an example of a simple unstable C*-algebra, the complexification of which is stable.