Boundaries of reduced C*-algebras of discrete groups

@article{Kalantar2014BoundariesOR,
  title={Boundaries of reduced C*-algebras of discrete groups},
  author={Mehrdad Kalantar and Matthew Kennedy},
  journal={arXiv: Operator Algebras},
  year={2014}
}
For a discrete group G, we consider the minimal C*-subalgebra of $\ell^\infty(G)$ that arises as the image of a unital positive G-equivariant projection. This algebra always exists and is unique up to isomorphism. It is trivial if and only if G is amenable. We prove that, more generally, it can be identified with the algebra $C(\partial_F G)$ of continuous functions on Furstenberg's universal G-boundary $\partial_F G$. This operator-algebraic construction of the Furstenberg boundary has a… 
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