The noncommutative Choquet boundary II: Hyperrigidity

dc.creatorArveson, William
dc.date2008-10-15
dc.date2009-05-28
dc.date.accessioned2026-07-07T13:18:22Z
dc.date.available2026-07-07T13:18:22Z
dc.descriptionA (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.descriptionA major revision, with new results in three new sections: substantial re-organization. 30 pages
dc.identifierhttps://arxiv.org/abs/0810.2751
dc.identifierhttp://arxiv.org/abs/0810.2751
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/231406
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.subject46L07, 46L52
dc.titleThe noncommutative Choquet boundary II: Hyperrigidity
dc.typetext

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