Skip Navigation


Proceedings of the London Mathematical Society Advance Access originally published online on July 5, 2007
Proceedings of the London Mathematical Society 2008 96(1):1-25; doi:10.1112/plms/pdm023
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
96/1/1    most recent
pdm023v1
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 Toms, A. S.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2007 London Mathematical Society

Stability in the Cuntz semigroup of a commutative C*-algebra

Andrew S. Toms

Department of Mathematics and Statistics
York University
4700 Keele Street
Toronto
Ontario, M3J 1P3
Canada

Received 12 September 2006. Revision received 1 March 2007.

Let A be a C*-algebra. The Cuntz semigroup W( A) is an analogue for positive elements of the semigroup V( A) of Murray-von Neumann equivalence classes of projections in matrices over A. We prove stability theorems for the Cuntz semigroup of a commutative C*-algebra which are analogues of classical stability theorems for topological vector bundles over compact Hausdorff spaces.

Let SDG denote the class of simple, unital, and infinite-dimensional AH algebras with slow dimension growth, and let A be an element of SDG. We apply our stability theorems to obtain the following:

  1. A has strict comparison of positive elements;
  2. W(A) is recovered functorially from the Elliott invariant of A;
  3. the lower semicontinuous dimension functions on A are weak-* dense in the dimension functions on A;
  4. the dimension functions on A form a Choquet simplex.
Statement (ii) confirms a conjecture of Perera and the author, while statements (iii) and (iv) confirm, for SDG, conjectures of Blackadar and Handelman from the early 1980s.

2000 Mathematics Subject Classification 46L35, 46L80.


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.