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March 25, 2015 By

Countable Saturation of Corona Algebras

C. R. Math. Rep. Acad. Sci. Canada Vol. 35 (2) 2013, pp. 35–56

June 30, 2013

Ilijas Farah, Department of Mathematics and Statistics, York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3, and Matematicki Institut, Kneza Mihaila 34, Belgrade, Serbia; e-mail: ifarah@mathstat.yorku.ca URL: http://www.math.yorku.ca/∼ifarah

Abstract/Résumé:

We present unified proofs of several properties of the corona of -unital C*-algebras such as AA-CRISP, SAW*, being sub--Stonean in the sense of Kirchberg, and the conclusion of Kasparov’s Technical Theorem. Although our results were obtained by considering C*-algebras as models of the logic for metric structures, the reader is not required to have any knowledge of model theory of metric structures (or model theory, or logic in general). The proofs involve analysis of the extent of model-theoretic saturation of corona algebras.

Nous présentons des démonstrations unifiées de plusieurs propriétés de la corona des C*-algèbres -unitales tel qu’AA-CRISP, SAW*, étant sous--Stonean au sens de Kirchberg, et la conclusion du théorème technique de Kasparov. Bien que nos résultats aient été obtenus en considérant les C*-algèbres comme modèles de la logique pour les structures métriques, le lecteur n’est pas requis d’avoir aucune connaissance de la théorie des modèles des structures métriques (ou la théorie des modèles, ou de la logique en général). Les démonstrations impliquent l’analyse de l’ampleur de la saturation modèle-théorétique des algèbres de corona.

Keywords:
AMS Subject Classification: General theory of $C^*$-algebras 46L05

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