On the Borel enveloping \(C^*\)-algebra of a \(C^*\)-algebra. (English) Zbl 0884.46038
L’auteur introduit et étudie la \(C^*\)-algèbre enveloppante borelienne d’une \(C^*\)-algèbre quelconque. On montre que le foncteur défini est exact et que la représentation atomique est fidèle. Si la \(C^*\)-algèbre initiale est commutative, la construction fournit la \(C^*\)-algèbre des fonctions complexes bornées boreliennes sur le spectre de l’algèbre donnée.
MSC:
| 46L05 | General theory of \(C^*\)-algebras |
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