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The noncommutative Choquet boundary II: Hyperrigidity

  • William ArvesonEmail author
Article

Abstract

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 AB(H) and every sequence of unital completely positive linear maps ϕ 1, ϕ 2,... 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 GG*. We present a variety of concrete applications and discuss prospects for further development.

Keywords

Irreducible Representation Compact Operator Boundary Representation Separable Hilbert Space Boundary Ideal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University Magnes Press 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, BerkeleyBerkeleyUSA

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