Operator System Nuclearity via $C^*$-envelopes
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2014
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| _version_ | 1866918265679249408 |
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| author | Gupta, Ved Prakash Luthra, Preeti |
| author_facet | Gupta, Ved Prakash Luthra, Preeti |
| contents | We prove that an operator system is (min, ess)-nuclear if its C*-envelope is nuclear. This allows us to deduce that an operator system associated to a generating set of countable discrete group by Farenick et al. 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 (resp., a finite graph) is (min, max)-nuclear if and only if the group is of order less than or equal to 3 (resp., every component of the graph is complete). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1408_4312 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Operator System Nuclearity via $C^*$-envelopes Gupta, Ved Prakash Luthra, Preeti Operator Algebras 46L06, 46L07, 47L25, 46M05, 46B28 We prove that an operator system is (min, ess)-nuclear if its C*-envelope is nuclear. This allows us to deduce that an operator system associated to a generating set of countable discrete group by Farenick et al. 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 (resp., a finite graph) is (min, max)-nuclear if and only if the group is of order less than or equal to 3 (resp., every component of the graph is complete). |
| title | Operator System Nuclearity via $C^*$-envelopes |
| topic | Operator Algebras 46L06, 46L07, 47L25, 46M05, 46B28 |
| url | https://arxiv.org/abs/1408.4312 |