The noncommutative Choquet boundary II: Hyperrigidity

By W. Arveson. 2008

108 citations recorded by the source corpus.

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 ⊆ B(H) and every sequence of unital completely positive linear maps ϕ1, ϕ2,... from B(H) to itself, $$\mathop {\lim }\limits_{n \to \infty } ||{\phi _n}(g) - g|| = 0,{\forall _g} \in G \Rightarrow \mathop {\lim }\limits_{n \to \infty } {\phi _n}(a) - a|| = 0,{\forall _a} \in A.$$ 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 ∪ G*. We present a variety of concrete applications and discuss prospects for further development.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a96b934d7ae4ba13486ca14dbcd9299dc105ab9a

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In Applied Mathematics

1. Adam H. Fuller
2. E. Kakariadis
3. K. Davidson
4. Michael Hartz

In Mathematical Physics

1. Adam H. Fuller
2. E. Kakariadis
3. K. Davidson
4. Orr Shalit
5. Michael Hartz
6. Martin J. Wainwright

Citations in the corpus

• Semicrossed Products of Operator Algebras by Semigroups (2014, background): “Arveson [10] calls an operator algebra A hyperrigid if for every ̊-representation π of CenvpAq, π|A has the unique extension property.”