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Finite-dimensional approximation properties for uniform Roe algebras
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abstract
We study property A for metric spaces $X$ with bounded geometry introduced by Guoliang Yu. Property A is an amenability-type condition, which is less restrictive than amenability for groups. The property has a connection with finite-dimensional approximation properties in the theory of operator algebras. It has been already known that property A of a metric space $X$ with bounded geometry is equivalent to nuclearity of the uniform Roe algebra C$^*_u(X)$. We prove that exactness and local reflexivity of C$^*_u(X)$ also characterize property A of $X$.
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Cited by 1 Pith paper
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Quasi-local Algebras and Asymptotic Expanders
The paper defines asymptotic expanders, characterizes quasi-locality of averaging projections via them, and proves the uniform quasi-local algebra is nuclear iff the space has Property A.
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