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The noncommutative Choquet boundary

2007
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Journal of The American Mathematical Society
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Let S be an operator system -- a self-adjoint linear subspace of a unital C*-algebra A such that contains 1 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 noncommutative counterpart of the Choquet boundary of a function system S⊆ C(X) that separates points

doi:10.1090/s0894-0347-07-00570-x
fatcat:xm6u33skm5g7pl7ykcfpzlfljy