Abstract
Let X be a noncompact discrete metric space with bounded geometry. Associated with X are two C*-algebras, the so-called uniform Roe algebra B*(X) and coarse Roe algebra C*(X), which arose from the index theory on noncompact complete Riemannian manifolds. In this paper, we describe the quasidiagonality of B*(X) and C*(X) in terms of coarse geometric invariants. Some necessary and sufficient conditions are given, which involve the Fredholm index and coarse connectedness of metric spaces.
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Wei, S. On the quasidiagonality of Roe algebras. Sci. China Math. 54, 1011–1018 (2011). https://doi.org/10.1007/s11425-011-4205-x
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DOI: https://doi.org/10.1007/s11425-011-4205-x