Perera, F., Toms, A., White, S. and Winter, W. (2014) The Cuntz semigroup and stability of close C*-algebras. Analysis and PDE, 7(4), pp. 929-952. (doi: 10.2140/apde.2014.7.929)
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Abstract
We prove that separable C*-algebras which are completely close in a natural uniform sense have isomorphic Cuntz semigroups, continuing a line of research developed by Kadison - Kastler, Christensen, and Khoshkam. This result has several applications: we are able to prove that the property of stability is preserved by close C*-algebras provided that one algebra has stable rank one; close C*-algebras must have affinely homeomorphic spaces of lower-semicontinuous quasitraces; strict comparison is preserved by sufficient closeness of C*-algebras. We also examine C*-algebras which have a positive answer to Kadison's Similarity Problem, as these algebras are completely close whenever they are close. A sample consequence is that sufficiently close C*-algebras have isomorphic Cuntz semigroups when one algebra absorbs the Jiang-Su algebra tensorially.<p></p>
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | White, Professor Stuart |
| Authors: | Perera, F., Toms, A., White, S., and Winter, W. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Analysis and PDE |
| Journal Abbr.: | Anal. PDE |
| Publisher: | Mathematical Sciences Publishers |
| ISSN: | 2157-5045 |
| ISSN (Online): | 1948-206X |
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