BOUNDARY REPRESENTATIONS FOR FAMILIES OF REPRESENTATIONS OF OPERATOR ALGEBRAS AND SPACES

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The noncommutative Choquet boundary II: Hyperrigidity (2008, background): “More recently, Dritschel and McCullough [DM05] gave a second proof of the existence of this ideal in general that is independent of the theory of injective envelopes.”
Operator Algebras for Multivariable Dynamics (2007, background): “In recent work, Dritschel and McCullough [14] show that themaximal representations of an operator algebra A are precisely those which extend (uniquely) to a ∗-representation of the C*-envelope, C∗env(A).”
Dilation theory, commutant lifting and semicrossed products (2011, methodology): “Dritschel and McCullough [27] establish the existence of extremals dominating ρ in each of these classes.”
Multiplier algebras of complete Nevanlinna–Pick spaces: Dilations, boundary representations and hyperrigidity (2016, methodology): “By Corollary 6.4, we conclude that there are only two possible isomorphism classes of C∗-envelopes for the algebras A(H) in this setting.”
Semicrossed Products of Operator Algebras by Semigroups (2014, background): “A modern independent description is given by Dritschel and McCullough [42] as the C*-algebra generated by a maximal completely isometric representation of A.”