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OPERATOR SYSTEM NUCLEARITY VIA
$C^{\ast }$ -ENVELOPES
Published online by Cambridge University Press: 11 May 2016
Abstract
We prove that an operator system is (min, ess)-nuclear if its $C^{\ast }$ -envelope is nuclear. This allows us to deduce that an operator system associated to a generating set of a countable discrete group by Farenick et al. [‘Operator systems from discrete groups’, Comm. Math. Phys.329(1) (2014), 207–238] is (min, ess)-nuclear if and only if the group is amenable. We also make a detailed comparison between ess and other operator system tensor products and show that an operator system associated to a minimal generating set of a finitely generated discrete group (respectively, a finite graph) is (min, max)-nuclear if and only if the group is of order less than or equal to three (respectively, every component of the graph is complete).
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 101 , Issue 3 , December 2016 , pp. 356 - 375
- Copyright
- © 2016 Australian Mathematical Publishing Association Inc.
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