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We introduce a generalization of expander graphs, which is called a weakexpander sequence. It is proved that a uniform Roe algebra of a weak expandersequence is not locally reflexive. It follows that uniform Roe algebras ofexpander graphs are not exact. We introduce the notion of a generalized boxspace to discuss box spaces and expander sequences in a unified framework. Keytools for the proof are amenable traces and measured groupoids associated togeneralized box spaces.

A generalization of expander graphs and local reflexivity of uniform Roe algebras