The Noncommutative Choquet Boundary Ii: Hyperrigidity
نویسنده
چکیده
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, lim n→∞ ‖φn(g)− g‖ = 0,∀g ∈ G =⇒ lim n→∞ ‖φn(a)− a‖ = 0, ∀a ∈ 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.
منابع مشابه
The Noncommutative Choquet Boundary
Let S be an operator system – a self-adjoint linear subspace of a unital C∗-algebra A such that 1 ∈ S and A = C∗(S) is generated by S. A boundary representation for S is an irreducible representation π of C∗(S) on a Hilbert space with the property that π S has a unique completely positive extension to C∗(S). The set ∂S of all (unitary equivalence classes of) boundary representations is the nonc...
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