On discrete twisted C*-dynamical systems, Hilbert C*-modules and regularity
We first give an overview of the basic theory for discrete unital twisted C*-dynamical systems and their covariant representations on Hilbert C*-modules. After introducing the notion of equivariant representations of such systems and their product with covariant representations, we prove a kind of F...
Verfasser: | |
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FB/Einrichtung: | FB 10: Mathematik und Informatik |
Dokumenttypen: | Artikel |
Medientypen: | Text |
Erscheinungsdatum: | 2012 |
Publikation in MIAMI: | 23.10.2012 |
Datum der letzten Änderung: | 14.04.2022 |
Quelle: | Münster Journal of Mathematics, 5 (2012), S. 183-208 |
Angaben zur Ausgabe: | [Electronic ed.] |
Fachgebiet (DDC): | 510: Mathematik |
Lizenz: | InC 1.0 |
Sprache: | English |
Format: | PDF-Dokument |
URN: | urn:nbn:de:hbz:6-88399587577 |
Permalink: | https://nbn-resolving.de/urn:nbn:de:hbz:6-88399587577 |
Onlinezugriff: | mjm_vol_5_10.pdf |
We first give an overview of the basic theory for discrete unital twisted C*-dynamical systems and their covariant representations on Hilbert C*-modules. After introducing the notion of equivariant representations of such systems and their product with covariant representations, we prove a kind of Fell absorption principle saying that the product of an induced regular equivariant representation with a covariant faithful representation is weakly equivalent to an induced regular covariant representation. This principle is the key to our main result, namely that a certain property, formally weaker than Exel’s approximation property, ensures that the system is regular, i.e., the associated full and reduced C*-crossed products are canonically isomorphic.