The noncommutative Choquet boundary II: Hyperrigidity
| dc.creator | Arveson, William | |
| dc.date | 2008-10-15 | |
| dc.date | 2009-05-28 | |
| dc.date.accessioned | 2026-07-07T13:18:22Z | |
| dc.date.available | 2026-07-07T13:18:22Z | |
| dc.description | A (finite or countably infinite) set G of generators of an abstract C*-algebra A is called hyperrigid if for every faithful representation of A on a Hilbert space $A\subseteq \mathcal B(H)$ and every sequence of unital completely positive linear maps $ϕ_1, ϕ_2,...$ from $\mathcal B(H)$ to itself, $$ \lim_{n\to\infty}\|ϕ_n(g)-g\|=0, \forall g\in G \implies \lim_{n\to\infty}\|ϕ_n(a)-a\|=0, \forall a\in A. $$ We show that one can determine whether a given set G of generators is hyperrigid by examining the noncommutative Choquet boundary of the operator space spanned by $G\cup G^*$. We present a variety of concrete applications and discuss prospects for further development. | |
| dc.description | A major revision, with new results in three new sections: substantial re-organization. 30 pages | |
| dc.identifier | https://arxiv.org/abs/0810.2751 | |
| dc.identifier | http://arxiv.org/abs/0810.2751 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/231406 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L07, 46L52 | |
| dc.title | The noncommutative Choquet boundary II: Hyperrigidity | |
| dc.type | text |