Skip Navigation


Proceedings of the London Mathematical Society Advance Access originally published online on November 23, 2007
Proceedings of the London Mathematical Society 2008 96(3):545-581; doi:10.1112/plms/pdm038
This Article
Right arrow FREE Full Text (PDF) Freely available
Right arrow All Versions of this Article:
96/3/545    most recent
pdm038v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Archbold, R.
Right arrow Articles by an Huef, A.
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2007 London Mathematical Society

Strength of convergence and multiplicities in the spectrum of a C*-dynamical system

Robert Archbold

Department of Mathematical Sciences
University of Aberdeen
Aberdeen AB24 3UE
Scotland
United Kingdom

Astrid an Huef

School of Mathematics and Statistics
University of New South Wales
Sydney, NSW 2052
Australia
astrid@unsw.edu.au

Received 7 December 2006. Revision received 3 April 2007.

We consider separable C*-dynamical systems (A, G,{alpha}) for which the induced action of the group G on the primitive ideal space Prim A of the C*-algebra A is free. We study how the representation theory of the associated crossed product C*-algebra A{rtimes}{alpha} G depends on the representation theory of A and the properties of the action of G on Prim A and the spectrum Â. Our main tools involve computations of upper and lower bounds on multiplicity numbers associated to irreducible representations of A{rtimes}{alpha} G. We apply our techniques to give necessary and sufficient conditions, in terms of A and the action of G, for A{rtimes}{alpha}G to be (i) a continuous-trace C*-algebra, (ii) a Fell C*-algebra and (iii) a bounded-trace C*-algebra. When G is amenable, we also give necessary and sufficient conditions for the crossed product C*-algebra A{rtimes}{alpha}G to be (iv) a liminal C*-algebra and (v) a Type I C*-algebra. The results in (i), (iii)–(v) extend some earlier special cases in which A was assumed to have the corresponding property.

2000 Mathematics Subject Classification 46L05, 46L30, 46L55, 54H15, 57S05.

This research was supported by grants from the Australian Research Council, the University of Aberdeen and the University of New South Wales.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.