Stability of Real $C^*$-Algebras
Printed: Dec 2011
Jeffrey L. Boersema,
We will give a characterization of stable real $C^*$-algebras
analogous to the one given for complex $C^*$-algebras by Hjelmborg
and Rørdam. 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.
stability, real C*-algebras
46L05 - General theory of $C^*$-algebras