Kechris, Alexander S. (1998) The descriptive classification of some classes of C∗-algebras. In: Proceedings of the Sixth Asian Logic Conference. World Scientific , River Edge, NJ, pp. 121-149. ISBN 9789810234324. https://resolver.caltech.edu/CaltechAUTHORS:20130522-083928827
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Abstract
We introduce here a parametrization of separable C*-algebras by a standard Borel space and study the descriptive complexity of various canonical classes of C*-algebras in this parametrization. This can be viewed as providing an analog of the corresponding classification of classes of von Neumann algebras (acting on a fixed separable Hilbert space) in the Effros Borel space of von Neumann algebras (see for example Nielsen [13]). However, in contrast with the von Neumann case, where most interesting classes (like: factors, type I, II, III, hyperfinite) turn out to be Borel, in the C*-algebra case many important classes turn out to be co-analytic but not Borel. This makes the situation more interesting from the set-theoretic point of view, and leads to further questions, like the construction of canonical co-analytic norms, which we also address here. Finally, we relate the above to work of Sutherland [17] on parametrization of Polish groups and indicate how one might be able to show that various familiar classes of (second countable) locally compact groups are non-Borel as well.
Item Type: | Book Section | ||||||
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Additional Information: | © 1998 World Scientific. We would like to thank E. Effros for many valuable conversations about this subject. Research and preparation of this paper were partially supported by NSF Grants DMS-9317509 and 9619880. | ||||||
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Record Number: | CaltechAUTHORS:20130522-083928827 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20130522-083928827 | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 38625 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | Tony Diaz | ||||||
Deposited On: | 23 May 2013 15:46 | ||||||
Last Modified: | 03 Oct 2019 04:59 |
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