# 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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