Continuous-trace Algebras from the Bundle Theoretic Point of View

Using various facts about principal bundles over a space, we give a unified treatment of several theorems about the structure of stable separable continuous-trace algebras, their automorphisms, and their AT-theory. We also present a classification of real continuous-trace algebras from the same point of view. 1980 Mathematics subject classification (Amer. Math. Soc.) (1985 Revision): 46 L 05, 46 L 35, 46 L 80, 46 M 20, 55 R 10, 19 K 99. This paper collects together a number of observations about continuous-trace C* -algebras, especially in the stable separable case. While I do not claim any great originality for any of these remarks, I have tried to do everything from the uniform point of view of the topology of bundles, which I have found helpful over the years. Thus I hope these comments will be of some value to others. I would like to thank the Centre for Mathematical Analysis, and in particular the organisers of the August 1987 miniconference on operator algebras and harmonic analysis, for helping to make this project possible. Parts of Section 3 below were presented at the conference on operator algebras in Santa Barbara, California, in 1986. This research was partially supported by the National Science Foundation of the U.S.A., Grant no. DMS-87-00551. The paper was written while the author was visiting the Centre for Mathematical Analysis at the Australian National University, Canberra, July-August, 1987. © 1989 Australian Mathematical Society 0263-6115/89 $A2.00 + 0.00