The Cuntz semigroup and stability of close C*-algebras

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.

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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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
596411The Cuntz Semigroup and the Fine Structure of Nuclear C*-AlgebrasStuart WhiteEngineering & Physical Sciences Research Council (EPSRC)EP/I019227/1M&S - MATHEMATICS