Stability of Real C*-Algebras

Boersema, Jeffrey L. ; Ruiz, Efren

Canadian mathematical bulletin, Tome 54 (2011) no. 4, pp. 593-606

Résumé

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 $\text{AF}$ -algebras and purely infinite C*-algebras. We will also provide an example of a simple unstable C*-algebra, the complexification of which is stable.

Détail

DOI : 10.4153/CMB-2011-019-0

Mots-clés : 46L05, stability, real C*-algebras

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