Abstract
We prove that separable -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 -algebras provided that one algebra has stable rank one; close -algebras must have affinely homeomorphic spaces of lower-semicontinuous quasitraces; strict comparison is preserved by sufficient closeness of -algebras. We also examine -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 -algebras have isomorphic Cuntz semigroups when one algebra absorbs the Jiang–Su algebra tensorially.
Citation
Francesc Perera. Andrew Toms. Stuart White. Wilhelm Winter. "The Cuntz semigroup and stability of close $C^*$-algebras." Anal. PDE 7 (4) 929 - 952, 2014. https://doi.org/10.2140/apde.2014.7.929
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